// Copyright (c) 2005  Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
​/*
 * Copyright (c) 2003-2005  Tom Wu
 * All Rights Reserved.
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
 * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
 * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
 * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
 * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
 * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
 * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 * In addition, the following condition applies:
 * All redistributions must retain an intact copy of this copyright notice
 * and disclaimer.
 */
​// Basic JavaScript BN library - subset useful for RSA encryption.
​// Bits per digit
var dbits;
​// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary&0xffffff)==0xefcafe);
​// (public) Constructor
function BigInteger(a,b,c) {
    if(a != null)
        if("number" == typeof a) this.fromNumber(a,b,c);
        else if(b == null && "string" != typeof a) this.fromString(a,256);
        else this.fromString(a,b);
}
​// return new, unset BigInteger
function nbi() { return new BigInteger(null); }
​// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
​// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i,x,w,j,c,n) {
    while(--n >= 0) {
        var v = x*this[i++]+w[j]+c;
        c = Math.floor(v/0x4000000);
        w[j++] = v&0x3ffffff;
    }
    return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i,x,w,j,c,n) {
    var xl = x&0x7fff, xh = x>>15;
    while(--n >= 0) {
        var l = this[i]&0x7fff;
        var h = this[i++]>>15;
        var m = xh*l+h*xl;
        l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
        c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
        w[j++] = l&0x3fffffff;
    }
    return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i,x,w,j,c,n) {
    var xl = x&0x3fff, xh = x>>14;
    while(--n >= 0) {
        var l = this[i]&0x3fff;
        var h = this[i++]>>14;
        var m = xh*l+h*xl;
        l = xl*l+((m&0x3fff)<<14)+w[j]+c;
        c = (l>>28)+(m>>14)+xh*h;
        w[j++] = l&0xfffffff;
    }
    return c;
}
if(j_lm) {
    BigInteger.prototype.am = am2;
    dbits = 30;
}
else if(j_lm) {
    BigInteger.prototype.am = am1;
    dbits = 26;
}
else { // Mozilla/Netscape seems to prefer am3
    BigInteger.prototype.am = am3;
    dbits = 28;
}
​BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
​var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
​// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = new Array();
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
​function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
    var c = BI_RC[s.charCodeAt(i)];
    return (c==null)?-1:c;
}
​// (protected) copy this to r
function bnpCopyTo(r) {
    for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
    r.t = this.t;
    r.s = this.s;
}
​// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
    this.t = 1;
    this.s = (x<0)?-1:0;
    if(x > 0) this[0] = x;
    else if(x < -1) this[0] = x+DV;
    else this.t = 0;
}
​// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
​// (protected) set from string and radix
function bnpFromString(s,b) {
    var k;
    if(b == 16) k = 4;
    else if(b == 8) k = 3;
    else if(b == 256) k = 8; // byte array
    else if(b == 2) k = 1;
    else if(b == 32) k = 5;
    else if(b == 4) k = 2;
    else { this.fromRadix(s,b); return; }
    this.t = 0;
    this.s = 0;
    var i = s.length, mi = false, sh = 0;
    while(--i >= 0) {
        var x = (k==8)?s[i]&0xff:intAt(s,i);
        if(x < 0) {
            if(s.charAt(i) == "-") mi = true;
            continue;
        }
        mi = false;
        if(sh == 0)
            this[this.t++] = x;
        else if(sh+k > this.DB) {
            this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
            this[this.t++] = (x>>(this.DB-sh));
        }
        else
            this[this.t-1] |= x<<sh;
        sh += k;
        if(sh >= this.DB) sh -= this.DB;
    }
    if(k == 8 && (s[0]&0x80) != 0) {
        this.s = -1;
        if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
    }
    this.clamp();
    if(mi) BigInteger.ZERO.subTo(this,this);
}
​
// (protected) clamp off excess high words
function bnpClamp() {
    var c = this.s&this.DM;
    while(this.t > 0 && this[this.t-1] == c) --this.t;
}​
// (public) return string representation in given radix
function bnToString(b) {
    if(this.s < 0) return "-"+this.negate().toString(b);
    var k;
    if(b == 16) k = 4;
    else if(b == 8) k = 3;
    else if(b == 2) k = 1;
    else if(b == 32) k = 5;
    else if(b == 4) k = 2;
    else return this.toRadix(b);
    var km = (1<<k)-1, d, m = false, r = "", i = this.t;
    var p = this.DB-(i*this.DB)%k;
    if(i-- > 0) {
        if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
        while(i >= 0) {
            if(p < k) {
                d = (this[i]&((1<<p)-1))<<(k-p);
                d |= this[--i]>>(p+=this.DB-k);
            }
            else {
                d = (this[i]>>(p-=k))&km;
                if(p <= 0) { p += this.DB; --i; }
            }
            if(d > 0) m = true;
            if(m) r += int2char(d);
        }
    }
    return m?r:"0";
}
​// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
​// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
​// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
    var r = this.s-a.s;
    if(r != 0) return r;
    var i = this.t;
    r = i-a.t;
    if(r != 0) return r;
    while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
    return 0;
}
​// returns bit length of the integer x
function nbits(x) {
    var r = 1, t;
    if((t=x>>>16) != 0) { x = t; r += 16; }
    if((t=x>>8) != 0) { x = t; r += 8; }
    if((t=x>>4) != 0) { x = t; r += 4; }
    if((t=x>>2) != 0) { x = t; r += 2; }
    if((t=x>>1) != 0) { x = t; r += 1; }
    return r;
}​
// (public) return the number of bits in "this"
function bnBitLength() {
    if(this.t <= 0) return 0;
    return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
​// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
    var i;
    for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
    for(i = n-1; i >= 0; --i) r[i] = 0;
    r.t = this.t+n;
    r.s = this.s;
}
​// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
    for(var i = n; i < this.t; ++i) r[i-n] = this[i];
    r.t = Math.max(this.t-n,0);
    r.s = this.s;
}
​// (protected) r = this << n
function bnpLShiftTo(n,r) {
    var bs = n%this.DB;
    var cbs = this.DB-bs;
    var bm = (1<<cbs)-1;
    var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
    for(i = this.t-1; i >= 0; --i) {
        r[i+ds+1] = (this[i]>>cbs)|c;
        c = (this[i]&bm)<<bs;
    }
    for(i = ds-1; i >= 0; --i) r[i] = 0;
    r[ds] = c;
    r.t = this.t+ds+1;
    r.s = this.s;
    r.clamp();
}
​// (protected) r = this >> n
function bnpRShiftTo(n,r) {
    r.s = this.s;
    var ds = Math.floor(n/this.DB);
    if(ds >= this.t) { r.t = 0; return; }
    var bs = n%this.DB;
    var cbs = this.DB-bs;
    var bm = (1<<bs)-1;
    r[0] = this[ds]>>bs;
    for(var i = ds+1; i < this.t; ++i) {
        r[i-ds-1] |= (this[i]&bm)<<cbs;
        r[i-ds] = this[i]>>bs;
    }
    if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
    r.t = this.t-ds;
    r.clamp();
}
​// (protected) r = this - a
function bnpSubTo(a,r) {
    var i = 0, c = 0, m = Math.min(a.t,this.t);
    while(i < m) {
        c += this[i]-a[i];
        r[i++] = c&this.DM;
        c >>= this.DB;
    }
    if(a.t < this.t) {
        c -= a.s;
        while(i < this.t) {
            c += this[i];
            r[i++] = c&this.DM;
            c >>= this.DB;
        }
        c += this.s;
    }
    else {
        c += this.s;
        while(i < a.t) {
            c -= a[i];
            r[i++] = c&this.DM;
            c >>= this.DB;
        }
        c -= a.s;
    }
    r.s = (c<0)?-1:0;
    if(c < -1) r[i++] = this.DV+c;
    else if(c > 0) r[i++] = c;
    r.t = i;
    r.clamp();
}
​
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
    var x = this.abs(), y = a.abs();
    var i = x.t;
    r.t = i+y.t;
    while(--i >= 0) r[i] = 0;
    for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
    r.s = 0;
    r.clamp();
    if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
​// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
    var x = this.abs();
    var i = r.t = 2*x.t;
    while(--i >= 0) r[i] = 0;
    for(i = 0; i < x.t-1; ++i) {
        var c = x.am(i,x[i],r,2*i,0,1);
        if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
            r[i+x.t] -= x.DV;
            r[i+x.t+1] = 1;
        }
    }
    if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
    r.s = 0;
    r.clamp();
}
​// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m.  q or r may be null.
function bnpDivRemTo(m,q,r) {
    var pm = m.abs();
    if(pm.t <= 0) return;
    var pt = this.abs();
    if(pt.t < pm.t) {
        if(q != null) q.fromInt(0);
        if(r != null) this.copyTo(r);
        return;
    }
    if(r == null) r = nbi();
    var y = nbi(), ts = this.s, ms = m.s;
    var nsh = this.DB-nbits(pm[pm.t-1]);    // normalize modulus
    if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
    else { pm.copyTo(y); pt.copyTo(r); }
    var ys = y.t;
    var y0 = y[ys-1];
    if(y0 == 0) return;
    var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
    var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
    var i = r.t, j = i-ys, t = (q==null)?nbi():q;
    y.dlShiftTo(j,t);
    if(r.compareTo(t) >= 0) {
        r[r.t++] = 1;
        r.subTo(t,r);
    }
    BigInteger.ONE.dlShiftTo(ys,t);
    t.subTo(y,y);    // "negative" y so we can replace sub with am later
    while(y.t < ys) y[y.t++] = 0;
    while(--j >= 0) {
        // Estimate quotient digit
        var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
        if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) {    // Try it out
            y.dlShiftTo(j,t);
            r.subTo(t,r);
            while(r[i] < --qd) r.subTo(t,r);
        }
    }
    if(q != null) {
        r.drShiftTo(ys,q);
        if(ts != ms) BigInteger.ZERO.subTo(q,q);
    }
    r.t = ys;
    r.clamp();
    if(nsh > 0) r.rShiftTo(nsh,r);    // Denormalize remainder
    if(ts < 0) BigInteger.ZERO.subTo(r,r);
}
​// (public) this mod a
function bnMod(a) {
    var r = nbi();
    this.abs().divRemTo(a,null,r);
    if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
    return r;
}
​// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
    if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
    else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x.divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
​Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
​// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
//         xy == 1 (mod m)
//         xy =  1+km
//   xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
    if(this.t < 1) return 0;
    var x = this[0];
    if((x&1) == 0) return 0;
    var y = x&3;        // y == 1/x mod 2^2
    y = (y*(2-(x&0xf)*y))&0xf;    // y == 1/x mod 2^4
    y = (y*(2-(x&0xff)*y))&0xff;    // y == 1/x mod 2^8
    y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;    // y == 1/x mod 2^16
    // last step - calculate inverse mod DV directly;
    // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
    y = (y*(2-x*y%this.DV))%this.DV;        // y == 1/x mod 2^dbits
    // we really want the negative inverse, and -DV < y < DV
    return (y>0)?this.DV-y:-y;
}
​// Montgomery reduction
function Montgomery(m) {
    this.m = m;
    this.mp = m.invDigit();
    this.mpl = this.mp&0x7fff;
    this.mph = this.mp>>15;
    this.um = (1<<(m.DB-15))-1;
    this.mt2 = 2*m.t;
}
​// xR mod m
function montConvert(x) {
    var r = nbi();
    x.abs().dlShiftTo(this.m.t,r);
    r.divRemTo(this.m,null,r);
    if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
    return r;
}
​// x/R mod m
function montRevert(x) {
    var r = nbi();
    x.copyTo(r);
    this.reduce(r);
    return r;
}
​// x = x/R mod m (HAC 14.32)
function montReduce(x) {
    while(x.t <= this.mt2)    // pad x so am has enough room later
        x[x.t++] = 0;
    for(var i = 0; i < this.m.t; ++i) {
        // faster way of calculating u0 = x[i]*mp mod DV
        var j = x[i]&0x7fff;
        var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
        // use am to combine the multiply-shift-add into one call
        j = i+this.m.t;
        x[j] += this.m.am(0,u0,x,i,0,this.m.t);
        // propagate carry
        while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
    }
    x.clamp();
    x.drShiftTo(this.m.t,x);
    if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
​// r = "x^2/R mod m"; x != r
function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
​// r = "xy/R mod m"; x,y != r
function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
​Montgomery.prototype.convert = montConvert;
Montgomery.prototype.revert = montRevert;
Montgomery.prototype.reduce = montReduce;
Montgomery.prototype.mulTo = montMulTo;
Montgomery.prototype.sqrTo = montSqrTo;
​// (protected) true iff this is even
function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
​// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
function bnpExp(e,z) {
    if(e > 0xffffffff || e < 1) return BigInteger.ONE;
    var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
    g.copyTo(r);
    while(--i >= 0) {
        z.sqrTo(r,r2);
        if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
        else { var t = r; r = r2; r2 = t; }
    }
    return z.revert(r);
}
​// (public) this^e % m, 0 <= e < 2^32
function bnModPowInt(e,m) {
    var z;
    if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
    return this.exp(e,z);
}
​
// protected
BigInteger.prototype.copyTo = bnpCopyTo;
BigInteger.prototype.fromInt = bnpFromInt;
BigInteger.prototype.fromString = bnpFromString;
BigInteger.prototype.clamp = bnpClamp;
BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
BigInteger.prototype.drShiftTo = bnpDRShiftTo;
BigInteger.prototype.lShiftTo = bnpLShiftTo;
BigInteger.prototype.rShiftTo = bnpRShiftTo;
BigInteger.prototype.subTo = bnpSubTo;
BigInteger.prototype.multiplyTo = bnpMultiplyTo;
BigInteger.prototype.squareTo = bnpSquareTo;
BigInteger.prototype.divRemTo = bnpDivRemTo;
BigInteger.prototype.invDigit = bnpInvDigit;
BigInteger.prototype.isEven = bnpIsEven;
BigInteger.prototype.exp = bnpExp;
​
// public
BigInteger.prototype.toString = bnToString;
BigInteger.prototype.negate = bnNegate;
BigInteger.prototype.abs = bnAbs;
BigInteger.prototype.compareTo = bnCompareTo;
BigInteger.prototype.bitLength = bnBitLength;
BigInteger.prototype.mod = bnMod;
BigInteger.prototype.modPowInt = bnModPowInt;
​
// "constants"
BigInteger.ZERO = nbv(0);
BigInteger.ONE = nbv(1);
​
​
// Copyright (c) 2005  Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
​
// Extended JavaScript BN functions, required for RSA private ops.
​
// (public)
function bnClone() { var r = nbi(); this.copyTo(r); return r; }
​
// (public) return value as integer
function bnIntValue() {
    if(this.s < 0) {
        if(this.t == 1) return this[0]-this.DV;
        else if(this.t == 0) return -1;
    }
    else if(this.t == 1) return this[0];
    else if(this.t == 0) return 0;
    // assumes 16 < DB < 32
    return ((this[1]&((1<<(32-this.DB))-1))<<this.DB)|this[0];
}
​
// (public) return value as byte
function bnByteValue() { return (this.t==0)?this.s:(this[0]<<24)>>24; }
​
// (public) return value as short (assumes DB>=16)
function bnShortValue() { return (this.t==0)?this.s:(this[0]<<16)>>16; }
​
// (protected) return x s.t. r^x < DV
function bnpChunkSize(r) { return Math.floor(Math.LN2*this.DB/Math.log(r)); }
​
// (public) 0 if this == 0, 1 if this > 0
function bnSigNum() {
    if(this.s < 0) return -1;
    else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
    else return 1;
}
​
// (protected) convert to radix string
function bnpToRadix(b) {
    if(b == null) b = 10;
    if(this.signum() == 0 || b < 2 || b > 36) return "0";
    var cs = this.chunkSize(b);
    var a = Math.pow(b,cs);
    var d = nbv(a), y = nbi(), z = nbi(), r = "";
    this.divRemTo(d,y,z);
    while(y.signum() > 0) {
        r = (a+z.intValue()).toString(b).substr(1) + r;
        y.divRemTo(d,y,z);
    }
    return z.intValue().toString(b) + r;
}
​
// (protected) convert from radix string
function bnpFromRadix(s,b) {
    this.fromInt(0);
    if(b == null) b = 10;
    var cs = this.chunkSize(b);
    var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
    for(var i = 0; i < s.length; ++i) {
        var x = intAt(s,i);
        if(x < 0) {
            if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
            continue;
        }
        w = b*w+x;
        if(++j >= cs) {
            this.dMultiply(d);
            this.dAddOffset(w,0);
            j = 0;
            w = 0;
        }
    }
    if(j > 0) {
        this.dMultiply(Math.pow(b,j));
        this.dAddOffset(w,0);
    }
    if(mi) BigInteger.ZERO.subTo(this,this);
}
​
// (protected) alternate constructor
function bnpFromNumber(a,b,c) {
    if("number" == typeof b) {
        // new BigInteger(int,int,RNG)
        if(a < 2) this.fromInt(1);
        else {
            this.fromNumber(a,c);
            if(!this.testBit(a-1))    // force MSB set
                this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
            if(this.isEven()) this.dAddOffset(1,0); // force odd
            while(!this.isProbablePrime(b)) {
                this.dAddOffset(2,0);
                if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
            }
        }
    }
    else {
        // new BigInteger(int,RNG)
        var x = new Array(), t = a&7;
        x.length = (a>>3)+1;
        b.nextBytes(x);
        if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
        this.fromString(x,256);
    }
}
​
// (public) convert to bigendian byte array
function bnToByteArray() {
    var i = this.t, r = new Array();
    r[0] = this.s;
    var p = this.DB-(i*this.DB)%8, d, k = 0;
    if(i-- > 0) {
        if(p < this.DB && (d = this[i]>>p) != (this.s&this.DM)>>p)
            r[k++] = d|(this.s<<(this.DB-p));
        while(i >= 0) {
            if(p < 8) {
                d = (this[i]&((1<<p)-1))<<(8-p);
                d |= this[--i]>>(p+=this.DB-8);
            }
            else {
                d = (this[i]>>(p-=8))&0xff;
                if(p <= 0) { p += this.DB; --i; }
            }
            if((d&0x80) != 0) d |= -256;
            if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
            if(k > 0 || d != this.s) r[k++] = d;
        }
    }
    return r;
}
​
function bnEquals(a) { return(this.compareTo(a)==0); }
function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
​
// (protected) r = this op a (bitwise)
function bnpBitwiseTo(a,op,r) {
    var i, f, m = Math.min(a.t,this.t);
    for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
    if(a.t < this.t) {
        f = a.s&this.DM;
        for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
        r.t = this.t;
    }
    else {
        f = this.s&this.DM;
        for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
        r.t = a.t;
    }
    r.s = op(this.s,a.s);
    r.clamp();
}
​
// (public) this & a
function op_and(x,y) { return x&y; }
function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
​
// (public) this | a
function op_or(x,y) { return x|y; }
function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
​
// (public) this ^ a
function op_xor(x,y) { return x^y; }
function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
​
// (public) this & ~a
function op_andnot(x,y) { return x&~y; }
function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
​
// (public) ~this
function bnNot() {
    var r = nbi();
    for(var i = 0; i < this.t; ++i) r[i] = this.DM&~this[i];
    r.t = this.t;
    r.s = ~this.s;
    return r;
}
​
// (public) this << n
function bnShiftLeft(n) {
    var r = nbi();
    if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
    return r;
}
​
// (public) this >> n
function bnShiftRight(n) {
    var r = nbi();
    if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
    return r;
}
​
// return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
    if(x == 0) return -1;
    var r = 0;
    if((x&0xffff) == 0) { x >>= 16; r += 16; }
    if((x&0xff) == 0) { x >>= 8; r += 8; }
    if((x&0xf) == 0) { x >>= 4; r += 4; }
    if((x&3) == 0) { x >>= 2; r += 2; }
    if((x&1) == 0) ++r;
    return r;
}
​
// (public) returns index of lowest 1-bit (or -1 if none)
function bnGetLowestSetBit() {
    for(var i = 0; i < this.t; ++i)
        if(this[i] != 0) return i*this.DB+lbit(this[i]);
    if(this.s < 0) return this.t*this.DB;
    return -1;
}
​
// return number of 1 bits in x
function cbit(x) {
    var r = 0;
    while(x != 0) { x &= x-1; ++r; }
    return r;
}
​
// (public) return number of set bits
function bnBitCount() {
    var r = 0, x = this.s&this.DM;
    for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
    return r;
}
​
// (public) true iff nth bit is set
function bnTestBit(n) {
    var j = Math.floor(n/this.DB);
    if(j >= this.t) return(this.s!=0);
    return((this[j]&(1<<(n%this.DB)))!=0);
}
​
// (protected) this op (1<<n)
function bnpChangeBit(n,op) {
    var r = BigInteger.ONE.shiftLeft(n);
    this.bitwiseTo(r,op,r);
    return r;
}
​
// (public) this | (1<<n)
function bnSetBit(n) { return this.changeBit(n,op_or); }
​
// (public) this & ~(1<<n)
function bnClearBit(n) { return this.changeBit(n,op_andnot); }
​
// (public) this ^ (1<<n)
function bnFlipBit(n) { return this.changeBit(n,op_xor); }
​
// (protected) r = this + a
function bnpAddTo(a,r) {
    var i = 0, c = 0, m = Math.min(a.t,this.t);
    while(i < m) {
        c += this[i]+a[i];
        r[i++] = c&this.DM;
        c >>= this.DB;
    }
    if(a.t < this.t) {
        c += a.s;
        while(i < this.t) {
            c += this[i];
            r[i++] = c&this.DM;
            c >>= this.DB;
        }
        c += this.s;
    }
    else {
        c += this.s;
        while(i < a.t) {
            c += a[i];
            r[i++] = c&this.DM;
            c >>= this.DB;
        }
        c += a.s;
    }
    r.s = (c<0)?-1:0;
    if(c > 0) r[i++] = c;
    else if(c < -1) r[i++] = this.DV+c;
    r.t = i;
    r.clamp();
}
​
// (public) this + a
function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
​
// (public) this - a
function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
​
// (public) this * a
function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
​
// (public) this / a
function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
​
// (public) this % a
function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
​
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
    var q = nbi(), r = nbi();
    this.divRemTo(a,q,r);
    return new Array(q,r);
}
​
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
    this[this.t] = this.am(0,n-1,this,0,0,this.t);
    ++this.t;
    this.clamp();
}
​
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
    while(this.t <= w) this[this.t++] = 0;
    this[w] += n;
    while(this[w] >= this.DV) {
        this[w] -= this.DV;
        if(++w >= this.t) this[this.t++] = 0;
        ++this[w];
    }
}
​
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
​
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
​
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
​
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
    var i = Math.min(this.t+a.t,n);
    r.s = 0; // assumes a,this >= 0
    r.t = i;
    while(i > 0) r[--i] = 0;
    var j;
    for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
    for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
    r.clamp();
}
​
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
    --n;
    var i = r.t = this.t+a.t-n;
    r.s = 0; // assumes a,this >= 0
    while(--i >= 0) r[i] = 0;
    for(i = Math.max(n-this.t,0); i < a.t; ++i)
        r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
    r.clamp();
    r.drShiftTo(1,r);
}
​
// Barrett modular reduction
function Barrett(m) {
    // setup Barrett
    this.r2 = nbi();
    this.q3 = nbi();
    BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
    this.mu = this.r2.divide(m);
    this.m = m;
}
​
function barrettConvert(x) {
    if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
    else if(x.compareTo(this.m) < 0) return x;
    else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
​
function barrettRevert(x) { return x; }
​
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
    x.drShiftTo(this.m.t-1,this.r2);
    if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
    this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
    this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
    while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
    x.subTo(this.r2,x);
    while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
​
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
​// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
​
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
​
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
    var i = e.bitLength(), k, r = nbv(1), z;
    if(i <= 0) return r;
    else if(i < 18) k = 1;
    else if(i < 48) k = 3;
    else if(i < 144) k = 4;
    else if(i < 768) k = 5;
    else k = 6;
    if(i < 8)
        z = new Classic(m);
    else if(m.isEven())
        z = new Barrett(m);
    else
        z = new Montgomery(m);
​
    // precomputation
    var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1;
    g[1] = z.convert(this);
    if(k > 1) {
        var g2 = nbi();
        z.sqrTo(g[1],g2);
        while(n <= km) {
            g[n] = nbi();
            z.mulTo(g2,g[n-2],g[n]);
            n += 2;
        }
    }
​
    var j = e.t-1, w, is1 = true, r2 = nbi(), t;
    i = nbits(e[j])-1;
    while(j >= 0) {
        if(i >= k1) w = (e[j]>>(i-k1))&km;
        else {
            w = (e[j]&((1<<(i+1))-1))<<(k1-i);
            if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
        }
​
        n = k;
        while((w&1) == 0) { w >>= 1; --n; }
        if((i -= n) < 0) { i += this.DB; --j; }
        if(is1) {    // ret == 1, don't bother squaring or multiplying it
            g[w].copyTo(r);
            is1 = false;
        }
        else {
            while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
            if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
            z.mulTo(r2,g[w],r);
        }
​
        while(j >= 0 && (e[j]&(1<<i)) == 0) {
            z.sqrTo(r,r2); t = r; r = r2; r2 = t;
            if(--i < 0) { i = this.DB-1; --j; }
        }
    }
    return z.revert(r);
}
​
// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
    var x = (this.s<0)?this.negate():this.clone();
    var y = (a.s<0)?a.negate():a.clone();
    if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
    var i = x.getLowestSetBit(), g = y.getLowestSetBit();
    if(g < 0) return x;
    if(i < g) g = i;
    if(g > 0) {
        x.rShiftTo(g,x);
        y.rShiftTo(g,y);
    }
    while(x.signum() > 0) {
        if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
        if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
        if(x.compareTo(y) >= 0) {
            x.subTo(y,x);
            x.rShiftTo(1,x);
        }
        else {
            y.subTo(x,y);
            y.rShiftTo(1,y);
        }
    }
    if(g > 0) y.lShiftTo(g,y);
    return y;
}
​
// (protected) this % n, n < 2^26
function bnpModInt(n) {
    if(n <= 0) return 0;
    var d = this.DV%n, r = (this.s<0)?n-1:0;
    if(this.t > 0)
        if(d == 0) r = this[0]%n;
        else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
    return r;
}
​
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
    var ac = m.isEven();
    if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
    var u = m.clone(), v = this.clone();
    var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
    while(u.signum() != 0) {
        while(u.isEven()) {
            u.rShiftTo(1,u);
            if(ac) {
                if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
                a.rShiftTo(1,a);
            }
            else if(!b.isEven()) b.subTo(m,b);
            b.rShiftTo(1,b);
        }
        while(v.isEven()) {
            v.rShiftTo(1,v);
            if(ac) {
                if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
                c.rShiftTo(1,c);
            }
            else if(!d.isEven()) d.subTo(m,d);
            d.rShiftTo(1,d);
        }
        if(u.compareTo(v) >= 0) {
            u.subTo(v,u);
            if(ac) a.subTo(c,a);
            b.subTo(d,b);
        }
        else {
            v.subTo(u,v);
            if(ac) c.subTo(a,c);
            d.subTo(b,d);
        }
    }
    if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
    if(d.compareTo(m) >= 0) return d.subtract(m);
    if(d.signum() < 0) d.addTo(m,d); else return d;
    if(d.signum() < 0) return d.add(m); else return d;
}
​
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
​
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
    var i, x = this.abs();
    if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
        for(i = 0; i < lowprimes.length; ++i)
            if(x[0] == lowprimes[i]) return true;
        return false;
    }
    if(x.isEven()) return false;
    i = 1;
    while(i < lowprimes.length) {
        var m = lowprimes[i], j = i+1;
        while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
        m = x.modInt(m);
        while(i < j) if(m%lowprimes[i++] == 0) return false;
    }
    return x.millerRabin(t);
}
​
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
    var n1 = this.subtract(BigInteger.ONE);
    var k = n1.getLowestSetBit();
    if(k <= 0) return false;
    var r = n1.shiftRight(k);
    t = (t+1)>>1;
    if(t > lowprimes.length) t = lowprimes.length;
    var a = nbi();
    for(var i = 0; i < t; ++i) {
        a.fromInt(lowprimes[i]);
        var y = a.modPow(r,this);
        if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
            var j = 1;
            while(j++ < k && y.compareTo(n1) != 0) {
                y = y.modPowInt(2,this);
                if(y.compareTo(BigInteger.ONE) == 0) return false;
            }
            if(y.compareTo(n1) != 0) return false;
        }
    }
    return true;
}
​
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
​
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
​
// BigInteger interfaces not implemented in jsbn:
​
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
​
​
​
​
var RSAPublicKey = function($modulus_hex, $encryptionExponent_hex) {
    this.modulus = new BigInteger( $modulus_hex, 16);
    this.encryptionExponent = new BigInteger( $encryptionExponent_hex, 16);
};
​
var Base64 = {
    base64: "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=",
    encode: function($input) {
        if (!$input) {
            return false;
        }
        var $output = "";
        var $chr1, $chr2, $chr3;
        var $enc1, $enc2, $enc3, $enc4;
        var $i = 0;
        do {
            $chr1 = $input.charCodeAt($i++);
            $chr2 = $input.charCodeAt($i++);
            $chr3 = $input.charCodeAt($i++);
            $enc1 = $chr1 >> 2;
            $enc2 = (($chr1 & 3) << 4) | ($chr2 >> 4);
            $enc3 = (($chr2 & 15) << 2) | ($chr3 >> 6);
            $enc4 = $chr3 & 63;
            if (isNaN($chr2)) $enc3 = $enc4 = 64;
            else if (isNaN($chr3)) $enc4 = 64;
            $output += this.base64.charAt($enc1) + this.base64.charAt($enc2) + this.base64.charAt($enc3) + this.base64.charAt($enc4);
        } while ($i < $input.length);
        return $output;
    },
    decode: function($input) {
        if(!$input) return false;
        $input = $input.replace(/[^A-Za-z0-9\+\/\=]/g, "");
        var $output = "";
        var $enc1, $enc2, $enc3, $enc4;
        var $i = 0;
        do {
            $enc1 = this.base64.indexOf($input.charAt($i++));
            $enc2 = this.base64.indexOf($input.charAt($i++));
            $enc3 = this.base64.indexOf($input.charAt($i++));
            $enc4 = this.base64.indexOf($input.charAt($i++));
            $output += String.fromCharCode(($enc1 << 2) | ($enc2 >> 4));
            if ($enc3 != 64) $output += String.fromCharCode((($enc2 & 15) << 4) | ($enc3 >> 2));
            if ($enc4 != 64) $output += String.fromCharCode((($enc3 & 3) << 6) | $enc4);
        } while ($i < $input.length);
        return $output;
    }
};
​
var Hex = {
    hex: "0123456789abcdef",
    encode: function($input) {
        if(!$input) return false;
        var $output = "";
        var $k;
        var $i = 0;
        do {
            $k = $input.charCodeAt($i++);
            $output += this.hex.charAt(($k >> 4) &0xf) + this.hex.charAt($k & 0xf);
        } while ($i < $input.length);
        return $output;
    },
    decode: function($input) {
        if(!$input) return false;
        $input = $input.replace(/[^0-9abcdef]/g, "");
        var $output = "";
        var $i = 0;
        do {
            $output += String.fromCharCode(((this.hex.indexOf($input.charAt($i++)) << 4) & 0xf0) | (this.hex.indexOf($input.charAt($i++)) & 0xf));
        } while ($i < $input.length);
        return $output;
    }
};
​
var RSA = {
​
    getPublicKey: function( $modulus_hex, $exponent_hex ) {
        return new RSAPublicKey( $modulus_hex, $exponent_hex );
    },
​
    encrypt: function($data, $pubkey) {
        if (!$pubkey) return false;
        $data = this.pkcs1pad2($data,($pubkey.modulus.bitLength()+7)>>3);
        if(!$data) return false;
        $data = $data.modPowInt($pubkey.encryptionExponent, $pubkey.modulus);
        if(!$data) return false;
        $data = $data.toString(16);
        if(($data.length & 1) == 1)
            $data = "0" + $data;
        return Base64.encode(Hex.decode($data));
    },
​
    pkcs1pad2: function($data, $keysize) {
        if($keysize < $data.length + 11)
            return null;
        var $buffer = [];
        var $i = $data.length - 1;
        while($i >= 0 && $keysize > 0)
            $buffer[--$keysize] = $data.charCodeAt($i--);
        $buffer[--$keysize] = 0;
        while($keysize > 2)
            $buffer[--$keysize] = Math.floor(Math.random()*254) + 1;
        $buffer[--$keysize] = 2;
        $buffer[--$keysize] = 0;
        return new BigInteger($buffer);
    }
};
​OnAuthCodeResponse = function(results, password) {
    // var form = this.m_$LogonForm[0];
    var pubKey = RSA.getPublicKey(results.publickey_mod, results.publickey_exp);
    // var username = this.m_strUsernameCanonical;
    // var password = form.elements['password'].value;
    password = password.replace(/[^\x00-\x7F]/g, '');
    // remove non-standard-ASCII characters
    var encryptedPassword = RSA.encrypt(password, pubKey);
    return encryptedPassword
};
​console.log(OnAuthCodeResponse({'success': 'True', 'publickey_mod': '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', 'publickey_exp': '010001', 'timestamp': '133267600000', 'token_gid': '27ddf868c7def6b4'}, '12345'))
​// Gq8LwJWnpwJS438pSVx7qnOW0gGGAv7gZbZKmbQtVcww4wVqck0FPUYScf8IyBz7DIbNawHVrx4lShLCS2oOPqxKNV6IybKESkARGXV4TqiVHF36oXejbO89zFWop5JDBeZl1nbV2y99fbSqAx2P/oxt3lm33xebkwc42KJqK1sAHK+dZ8YVT1Ji9J3JNeTVZvoH/4I5oRkb2ai5DsURllQkGvut3b9eGx6MSumCTp0YCVGjE4oE9WSq8Gvq7sD7F8QNobfRGUKk1TvcYmeqwDtSTGQWascbAic7+/yKV0ej2AyHyIQ/nnUMWjI4HWDRAqxyAHKkB6mPFLKKJZiQLQ==

import time
​import execjs
import requests
​login_url = 'https://store.steampowered.com/login/dologin/'
get_rsa_key_url = 'https://store.steampowered.com/login/getrsakey/'
​headers = {
    'Host': 'store.steampowered.com',
    'Origin': 'https://store.steampowered.com',
    'Referer': 'https://store.steampowered.com/login/?redir=&redir_ssl=1&snr=1_4_4__global-header',
    'User-Agent': 'Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/91.0.4472.124 Safari/537.36Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/94.0.4606.71 Safari/537.36'
}
session = requests.session()
​def get_rsa_key(username):
    data = {
        'donotcache': str(int(time.time() * 1000)),
        'username': username
    }
    response = session.post(url=get_rsa_key_url, data=data, headers=headers).json()
    print(response)
    return response
​def get_encrypted_password(password, rsa_key_dict):
    f = open('steam.js', 'r', encoding='utf-8')
    steampowered_js = f.read()
    f.close()
    encrypted_password = execjs.compile(steampowered_js).call('OnAuthCodeResponse', password, rsa_key_dict)
    return encrypted_password​
def login(username, encrypted_password, rsa_key_dict):
    data = {
        'donotcache': str(int(time.time() * 1000)),
        'password': encrypted_password,
        'username': username,
        'twofactorcode': '',
        'emailauth': '',
        'loginfriendlyname': '',
        'emailsteamid': '',
        'rsatimestamp': rsa_key_dict['timestamp'],
        'remember_login': False,
        'tokentype': '-1'
    }
    print(data)
    response = session.post(url=login_url, data=data, headers=headers)
    print(response.text)
​def main():
    username = input('請輸入登錄賬號: ')
    password = input('請輸入登錄密碼: ')
​    # 獲取 RSA 加密所需 key 等信息
    rsa_key_dict = get_rsa_key(username)
    # 獲取加密后的密碼
    encrypted_password = get_encrypted_password(password, rsa_key_dict)
    # print(encrypted_password)
    # 攜帶 用戶名、加密后的密碼、cookies、驗證碼等登錄
    login(username, encrypted_password, rsa_key_dict)
​if __name__ == '__main__':
    main()