// Downloaded from http://www-cs-students.stanford.edu/~tjw/jsbn/ by Jeremy White on 6/1/2012
  
  /*
   * 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 && (navigator.appName == "Microsoft Internet Explorer")) {
    BigInteger.prototype.am = am2;
    dbits = 30;
  }
  else if(j_lm && (navigator.appName != "Netscape")) {
    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);