var dbits,canary=0xdeadbeefcafe,j_lm=15715070==(16777215&canary);function BigInteger(t,e,r){null!=t&&("number"==typeof t?this.fromNumber(t,e,r):null==e&&"string"!=typeof t?this.fromString(t,256):this.fromString(t,e))}function nbi(){return new BigInteger(null)}function am1(t,e,r,n,i,o){for(;--o>=0;){var a=e*this[t++]+r[n]+i;i=Math.floor(a/67108864),r[n++]=67108863&a}return i}function am2(t,e,r,n,i,o){for(var a=32767&e,s=e>>15;--o>=0;){var l=32767&this[t],c=this[t++]>>15,u=s*l+c*a;i=((l=a*l+((32767&u)<<15)+r[n]+(1073741823&i))>>>30)+(u>>>15)+s*c+(i>>>30),r[n++]=1073741823&l}return i}function am3(t,e,r,n,i,o){for(var a=16383&e,s=e>>14;--o>=0;){var l=16383&this[t],c=this[t++]>>14,u=s*l+c*a;i=((l=a*l+((16383&u)<<14)+r[n]+i)>>28)+(u>>14)+s*c,r[n++]=268435455&l}return i}j_lm&&"Microsoft Internet Explorer"==navigator.appName?(BigInteger.prototype.am=am2,dbits=30):j_lm&&"Netscape"!=navigator.appName?(BigInteger.prototype.am=am1,dbits=26):(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;var rr,vv,BI_RM="0123456789abcdefghijklmnopqrstuvwxyz",BI_RC=new Array;for(rr="0".charCodeAt(0),vv=0;vv<=9;++vv)BI_RC[rr++]=vv;for(rr="a".charCodeAt(0),vv=10;vv<36;++vv)BI_RC[rr++]=vv;for(rr="A".charCodeAt(0),vv=10;vv<36;++vv)BI_RC[rr++]=vv;function int2char(t){return BI_RM.charAt(t)}function intAt(t,e){var r=BI_RC[t.charCodeAt(e)];return null==r?-1:r}function bnpCopyTo(t){for(var e=this.t-1;e>=0;--e)t[e]=this[e];t.t=this.t,t.s=this.s}function bnpFromInt(t){this.t=1,this.s=t<0?-1:0,t>0?this[0]=t:t<-1?this[0]=t+DV:this.t=0}function nbv(t){var e=nbi();return e.fromInt(t),e}function bnpFromString(t,e){var r;if(16==e)r=4;else if(8==e)r=3;else if(256==e)r=8;else if(2==e)r=1;else if(32==e)r=5;else{if(4!=e)return void this.fromRadix(t,e);r=2}this.t=0,this.s=0;for(var n=t.length,i=!1,o=0;--n>=0;){var a=8==r?255&t[n]:intAt(t,n);a<0?"-"==t.charAt(n)&&(i=!0):(i=!1,0==o?this[this.t++]=a:o+r>this.DB?(this[this.t-1]|=(a&(1<<this.DB-o)-1)<<o,this[this.t++]=a>>this.DB-o):this[this.t-1]|=a<<o,(o+=r)>=this.DB&&(o-=this.DB))}8==r&&128&t[0]&&(this.s=-1,o>0&&(this[this.t-1]|=(1<<this.DB-o)-1<<o)),this.clamp(),i&&BigInteger.ZERO.subTo(this,this)}function bnpClamp(){for(var t=this.s&this.DM;this.t>0&&this[this.t-1]==t;)--this.t}function bnToString(t){if(this.s<0)return"-"+this.negate().toString(t);var e;if(16==t)e=4;else if(8==t)e=3;else if(2==t)e=1;else if(32==t)e=5;else if(64==t)e=6;else{if(4!=t)return this.toRadix(t);e=2}var r,n=(1<<e)-1,i=!1,o="",a=this.t,s=this.DB-a*this.DB%e;if(a-- >0)for(s<this.DB&&(r=this[a]>>s)>0&&(i=!0,o=int2char(r));a>=0;)s<e?(r=(this[a]&(1<<s)-1)<<e-s,r|=this[--a]>>(s+=this.DB-e)):(r=this[a]>>(s-=e)&n,s<=0&&(s+=this.DB,--a)),r>0&&(i=!0),i&&(o+=int2char(r));return i?o:"0"}function bnNegate(){var t=nbi();return BigInteger.ZERO.subTo(this,t),t}function bnAbs(){return this.s<0?this.negate():this}function bnCompareTo(t){var e=this.s-t.s;if(0!=e)return e;var r=this.t;if(0!=(e=r-t.t))return e;for(;--r>=0;)if(0!=(e=this[r]-t[r]))return e;return 0}function nbits(t){var e,r=1;return 0!=(e=t>>>16)&&(t=e,r+=16),0!=(e=t>>8)&&(t=e,r+=8),0!=(e=t>>4)&&(t=e,r+=4),0!=(e=t>>2)&&(t=e,r+=2),0!=(e=t>>1)&&(t=e,r+=1),r}function bnBitLength(){return this.t<=0?0:this.DB*(this.t-1)+nbits(this[this.t-1]^this.s&this.DM)}function bnpDLShiftTo(t,e){var r;for(r=this.t-1;r>=0;--r)e[r+t]=this[r];for(r=t-1;r>=0;--r)e[r]=0;e.t=this.t+t,e.s=this.s}function bnpDRShiftTo(t,e){for(var r=t;r<this.t;++r)e[r-t]=this[r];e.t=Math.max(this.t-t,0),e.s=this.s}function bnpLShiftTo(t,e){var r,n=t%this.DB,i=this.DB-n,o=(1<<i)-1,a=Math.floor(t/this.DB),s=this.s<<n&this.DM;for(r=this.t-1;r>=0;--r)e[r+a+1]=this[r]>>i|s,s=(this[r]&o)<<n;for(r=a-1;r>=0;--r)e[r]=0;e[a]=s,e.t=this.t+a+1,e.s=this.s,e.clamp()}function bnpRShiftTo(t,e){e.s=this.s;var r=Math.floor(t/this.DB);if(r>=this.t)e.t=0;else{var n=t%this.DB,i=this.DB-n,o=(1<<n)-1;e[0]=this[r]>>n;for(var a=r+1;a<this.t;++a)e[a-r-1]|=(this[a]&o)<<i,e[a-r]=this[a]>>n;n>0&&(e[this.t-r-1]|=(this.s&o)<<i),e.t=this.t-r,e.clamp()}}function bnpSubTo(t,e){for(var r=0,n=0,i=Math.min(t.t,this.t);r<i;)n+=this[r]-t[r],e[r++]=n&this.DM,n>>=this.DB;if(t.t<this.t){for(n-=t.s;r<this.t;)n+=this[r],e[r++]=n&this.DM,n>>=this.DB;n+=this.s}else{for(n+=this.s;r<t.t;)n-=t[r],e[r++]=n&this.DM,n>>=this.DB;n-=t.s}e.s=n<0?-1:0,n<-1?e[r++]=this.DV+n:n>0&&(e[r++]=n),e.t=r,e.clamp()}function bnpMultiplyTo(t,e){var r=this.abs(),n=t.abs(),i=r.t;for(e.t=i+n.t;--i>=0;)e[i]=0;for(i=0;i<n.t;++i)e[i+r.t]=r.am(0,n[i],e,i,0,r.t);e.s=0,e.clamp(),this.s!=t.s&&BigInteger.ZERO.subTo(e,e)}function bnpSquareTo(t){for(var e=this.abs(),r=t.t=2*e.t;--r>=0;)t[r]=0;for(r=0;r<e.t-1;++r){var n=e.am(r,e[r],t,2*r,0,1);(t[r+e.t]+=e.am(r+1,2*e[r],t,2*r+1,n,e.t-r-1))>=e.DV&&(t[r+e.t]-=e.DV,t[r+e.t+1]=1)}t.t>0&&(t[t.t-1]+=e.am(r,e[r],t,2*r,0,1)),t.s=0,t.clamp()}function bnpDivRemTo(t,e,r){var n=t.abs();if(!(n.t<=0)){var i=this.abs();if(i.t<n.t)return null!=e&&e.fromInt(0),void(null!=r&&this.copyTo(r));null==r&&(r=nbi());var o=nbi(),a=this.s,s=t.s,l=this.DB-nbits(n[n.t-1]);l>0?(n.lShiftTo(l,o),i.lShiftTo(l,r)):(n.copyTo(o),i.copyTo(r));var c=o.t,u=o[c-1];if(0!=u){var d=u*(1<<this.F1)+(c>1?o[c-2]>>this.F2:0),p=this.FV/d,h=(1<<this.F1)/d,f=1<<this.F2,g=r.t,m=g-c,_=null==e?nbi():e;for(o.dlShiftTo(m,_),r.compareTo(_)>=0&&(r[r.t++]=1,r.subTo(_,r)),BigInteger.ONE.dlShiftTo(c,_),_.subTo(o,o);o.t<c;)o[o.t++]=0;for(;--m>=0;){var b=r[--g]==u?this.DM:Math.floor(r[g]*p+(r[g-1]+f)*h);if((r[g]+=o.am(0,b,r,m,0,c))<b)for(o.dlShiftTo(m,_),r.subTo(_,r);r[g]<--b;)r.subTo(_,r)}null!=e&&(r.drShiftTo(c,e),a!=s&&BigInteger.ZERO.subTo(e,e)),r.t=c,r.clamp(),l>0&&r.rShiftTo(l,r),a<0&&BigInteger.ZERO.subTo(r,r)}}}function bnMod(t){var e=nbi();return this.abs().divRemTo(t,null,e),this.s<0&&e.compareTo(BigInteger.ZERO)>0&&t.subTo(e,e),e}function Classic(t){this.m=t}function cConvert(t){return t.s<0||t.compareTo(this.m)>=0?t.mod(this.m):t}function cRevert(t){return t}function cReduce(t){t.divRemTo(this.m,null,t)}function cMulTo(t,e,r){t.multiplyTo(e,r),this.reduce(r)}function cSqrTo(t,e){t.squareTo(e),this.reduce(e)}function bnpInvDigit(){if(this.t<1)return 0;var t=this[0];if(!(1&t))return 0;var e=3&t;return(e=(e=(e=(e=e*(2-(15&t)*e)&15)*(2-(255&t)*e)&255)*(2-((65535&t)*e&65535))&65535)*(2-t*e%this.DV)%this.DV)>0?this.DV-e:-e}function Montgomery(t){this.m=t,this.mp=t.invDigit(),this.mpl=32767&this.mp,this.mph=this.mp>>15,this.um=(1<<t.DB-15)-1,this.mt2=2*t.t}function montConvert(t){var e=nbi();return t.abs().dlShiftTo(this.m.t,e),e.divRemTo(this.m,null,e),t.s<0&&e.compareTo(BigInteger.ZERO)>0&&this.m.subTo(e,e),e}function montRevert(t){var e=nbi();return t.copyTo(e),this.reduce(e),e}function montReduce(t){for(;t.t<=this.mt2;)t[t.t++]=0;for(var e=0;e<this.m.t;++e){var r=32767&t[e],n=r*this.mpl+((r*this.mph+(t[e]>>15)*this.mpl&this.um)<<15)&t.DM;for(t[r=e+this.m.t]+=this.m.am(0,n,t,e,0,this.m.t);t[r]>=t.DV;)t[r]-=t.DV,t[++r]++}t.clamp(),t.drShiftTo(this.m.t,t),t.compareTo(this.m)>=0&&t.subTo(this.m,t)}function montSqrTo(t,e){t.squareTo(e),this.reduce(e)}function montMulTo(t,e,r){t.multiplyTo(e,r),this.reduce(r)}function bnpIsEven(){return 0==(this.t>0?1&this[0]:this.s)}function bnpExp(t,e){if(t>4294967295||t<1)return BigInteger.ONE;var r=nbi(),n=nbi(),i=e.convert(this),o=nbits(t)-1;for(i.copyTo(r);--o>=0;)if(e.sqrTo(r,n),(t&1<<o)>0)e.mulTo(n,i,r);else{var a=r;r=n,n=a}return e.revert(r)}function bnModPowInt(t,e){var r;return r=t<256||e.isEven()?new Classic(e):new Montgomery(e),this.exp(t,r)}function bnClone(){var t=nbi();return this.copyTo(t),t}function bnIntValue(){if(this.s<0){if(1==this.t)return this[0]-this.DV;if(0==this.t)return-1}else{if(1==this.t)return this[0];if(0==this.t)return 0}return(this[1]&(1<<32-this.DB)-1)<<this.DB|this[0]}function bnByteValue(){return 0==this.t?this.s:this[0]<<24>>24}function bnShortValue(){return 0==this.t?this.s:this[0]<<16>>16}function bnpChunkSize(t){return Math.floor(Math.LN2*this.DB/Math.log(t))}function bnSigNum(){return this.s<0?-1:this.t<=0||1==this.t&&this[0]<=0?0:1}function bnpToRadix(t){if(null==t&&(t=10),0==this.signum()||t<2||t>36)return"0";var e=this.chunkSize(t),r=Math.pow(t,e),n=nbv(r),i=nbi(),o=nbi(),a="";for(this.divRemTo(n,i,o);i.signum()>0;)a=(r+o.intValue()).toString(t).substr(1)+a,i.divRemTo(n,i,o);return o.intValue().toString(t)+a}function bnpFromRadix(t,e){this.fromInt(0),null==e&&(e=10);for(var r=this.chunkSize(e),n=Math.pow(e,r),i=!1,o=0,a=0,s=0;s<t.length;++s){var l=intAt(t,s);l<0?"-"==t.charAt(s)&&0==this.signum()&&(i=!0):(a=e*a+l,++o>=r&&(this.dMultiply(n),this.dAddOffset(a,0),o=0,a=0))}o>0&&(this.dMultiply(Math.pow(e,o)),this.dAddOffset(a,0)),i&&BigInteger.ZERO.subTo(this,this)}function bnpFromNumber(t,e,r){if("number"==typeof e)if(t<2)this.fromInt(1);else for(this.fromNumber(t,r),this.testBit(t-1)||this.bitwiseTo(BigInteger.ONE.shiftLeft(t-1),op_or,this),this.isEven()&&this.dAddOffset(1,0);!this.isProbablePrime(e);)this.dAddOffset(2,0),this.bitLength()>t&&this.subTo(BigInteger.ONE.shiftLeft(t-1),this);else{var n=new Array,i=7&t;n.length=1+(t>>3),e.nextBytes(n),i>0?n[0]&=(1<<i)-1:n[0]=0,this.fromString(n,256)}}function bnToByteArray(){var t=this.t,e=new Array;e[0]=this.s;var r,n=this.DB-t*this.DB%8,i=0;if(t-- >0)for(n<this.DB&&(r=this[t]>>n)!=(this.s&this.DM)>>n&&(e[i++]=r|this.s<<this.DB-n);t>=0;)n<8?(r=(this[t]&(1<<n)-1)<<8-n,r|=this[--t]>>(n+=this.DB-8)):(r=this[t]>>(n-=8)&255,n<=0&&(n+=this.DB,--t)),128&r&&(r|=-256),0==i&&(128&this.s)!=(128&r)&&++i,(i>0||r!=this.s)&&(e[i++]=r);return e}function bnEquals(t){return 0==this.compareTo(t)}function bnMin(t){return this.compareTo(t)<0?this:t}function bnMax(t){return this.compareTo(t)>0?this:t}function bnpBitwiseTo(t,e,r){var n,i,o=Math.min(t.t,this.t);for(n=0;n<o;++n)r[n]=e(this[n],t[n]);if(t.t<this.t){for(i=t.s&this.DM,n=o;n<this.t;++n)r[n]=e(this[n],i);r.t=this.t}else{for(i=this.s&this.DM,n=o;n<t.t;++n)r[n]=e(i,t[n]);r.t=t.t}r.s=e(this.s,t.s),r.clamp()}function op_and(t,e){return t&e}function bnAnd(t){var e=nbi();return this.bitwiseTo(t,op_and,e),e}function op_or(t,e){return t|e}function bnOr(t){var e=nbi();return this.bitwiseTo(t,op_or,e),e}function op_xor(t,e){return t^e}function bnXor(t){var e=nbi();return this.bitwiseTo(t,op_xor,e),e}function op_andnot(t,e){return t&~e}function bnAndNot(t){var e=nbi();return this.bitwiseTo(t,op_andnot,e),e}function bnNot(){for(var t=nbi(),e=0;e<this.t;++e)t[e]=this.DM&~this[e];return t.t=this.t,t.s=~this.s,t}function bnShiftLeft(t){var e=nbi();return t<0?this.rShiftTo(-t,e):this.lShiftTo(t,e),e}function bnShiftRight(t){var e=nbi();return t<0?this.lShiftTo(-t,e):this.rShiftTo(t,e),e}function lbit(t){if(0==t)return-1;var e=0;return 65535&t||(t>>=16,e+=16),255&t||(t>>=8,e+=8),15&t||(t>>=4,e+=4),3&t||(t>>=2,e+=2),1&t||++e,e}function bnGetLowestSetBit(){for(var t=0;t<this.t;++t)if(0!=this[t])return t*this.DB+lbit(this[t]);return this.s<0?this.t*this.DB:-1}function cbit(t){for(var e=0;0!=t;)t&=t-1,++e;return e}function bnBitCount(){for(var t=0,e=this.s&this.DM,r=0;r<this.t;++r)t+=cbit(this[r]^e);return t}function bnTestBit(t){var e=Math.floor(t/this.DB);return e>=this.t?0!=this.s:!!(this[e]&1<<t%this.DB)}function bnpChangeBit(t,e){var r=BigInteger.ONE.shiftLeft(t);return this.bitwiseTo(r,e,r),r}function bnSetBit(t){return this.changeBit(t,op_or)}function bnClearBit(t){return this.changeBit(t,op_andnot)}function bnFlipBit(t){return this.changeBit(t,op_xor)}function bnpAddTo(t,e){for(var r=0,n=0,i=Math.min(t.t,this.t);r<i;)n+=this[r]+t[r],e[r++]=n&this.DM,n>>=this.DB;if(t.t<this.t){for(n+=t.s;r<this.t;)n+=this[r],e[r++]=n&this.DM,n>>=this.DB;n+=this.s}else{for(n+=this.s;r<t.t;)n+=t[r],e[r++]=n&this.DM,n>>=this.DB;n+=t.s}e.s=n<0?-1:0,n>0?e[r++]=n:n<-1&&(e[r++]=this.DV+n),e.t=r,e.clamp()}function bnAdd(t){var e=nbi();return this.addTo(t,e),e}function bnSubtract(t){var e=nbi();return this.subTo(t,e),e}function bnMultiply(t){var e=nbi();return this.multiplyTo(t,e),e}function bnSquare(){var t=nbi();return this.squareTo(t),t}function bnDivide(t){var e=nbi();return this.divRemTo(t,e,null),e}function bnRemainder(t){var e=nbi();return this.divRemTo(t,null,e),e}function bnDivideAndRemainder(t){var e=nbi(),r=nbi();return this.divRemTo(t,e,r),new Array(e,r)}function bnpDMultiply(t){this[this.t]=this.am(0,t-1,this,0,0,this.t),++this.t,this.clamp()}function bnpDAddOffset(t,e){if(0!=t){for(;this.t<=e;)this[this.t++]=0;for(this[e]+=t;this[e]>=this.DV;)this[e]-=this.DV,++e>=this.t&&(this[this.t++]=0),++this[e]}}function NullExp(){}function nNop(t){return t}function nMulTo(t,e,r){t.multiplyTo(e,r)}function nSqrTo(t,e){t.squareTo(e)}function bnPow(t){return this.exp(t,new NullExp)}function bnpMultiplyLowerTo(t,e,r){var n,i=Math.min(this.t+t.t,e);for(r.s=0,r.t=i;i>0;)r[--i]=0;for(n=r.t-this.t;i<n;++i)r[i+this.t]=this.am(0,t[i],r,i,0,this.t);for(n=Math.min(t.t,e);i<n;++i)this.am(0,t[i],r,i,0,e-i);r.clamp()}function bnpMultiplyUpperTo(t,e,r){--e;var n=r.t=this.t+t.t-e;for(r.s=0;--n>=0;)r[n]=0;for(n=Math.max(e-this.t,0);n<t.t;++n)r[this.t+n-e]=this.am(e-n,t[n],r,0,0,this.t+n-e);r.clamp(),r.drShiftTo(1,r)}function Barrett(t){this.r2=nbi(),this.q3=nbi(),BigInteger.ONE.dlShiftTo(2*t.t,this.r2),this.mu=this.r2.divide(t),this.m=t}function barrettConvert(t){if(t.s<0||t.t>2*this.m.t)return t.mod(this.m);if(t.compareTo(this.m)<0)return t;var e=nbi();return t.copyTo(e),this.reduce(e),e}function barrettRevert(t){return t}function barrettReduce(t){for(t.drShiftTo(this.m.t-1,this.r2),t.t>this.m.t+1&&(t.t=this.m.t+1,t.clamp()),this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3),this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);t.compareTo(this.r2)<0;)t.dAddOffset(1,this.m.t+1);for(t.subTo(this.r2,t);t.compareTo(this.m)>=0;)t.subTo(this.m,t)}function barrettSqrTo(t,e){t.squareTo(e),this.reduce(e)}function barrettMulTo(t,e,r){t.multiplyTo(e,r),this.reduce(r)}function bnModPow(t,e){var r,n,i=t.bitLength(),o=nbv(1);if(i<=0)return o;r=i<18?1:i<48?3:i<144?4:i<768?5:6,n=i<8?new Classic(e):e.isEven()?new Barrett(e):new Montgomery(e);var a=new Array,s=3,l=r-1,c=(1<<r)-1;if(a[1]=n.convert(this),r>1){var u=nbi();for(n.sqrTo(a[1],u);s<=c;)a[s]=nbi(),n.mulTo(u,a[s-2],a[s]),s+=2}var d,p,h=t.t-1,f=!0,g=nbi();for(i=nbits(t[h])-1;h>=0;){for(i>=l?d=t[h]>>i-l&c:(d=(t[h]&(1<<i+1)-1)<<l-i,h>0&&(d|=t[h-1]>>this.DB+i-l)),s=r;!(1&d);)d>>=1,--s;if((i-=s)<0&&(i+=this.DB,--h),f)a[d].copyTo(o),f=!1;else{for(;s>1;)n.sqrTo(o,g),n.sqrTo(g,o),s-=2;s>0?n.sqrTo(o,g):(p=o,o=g,g=p),n.mulTo(g,a[d],o)}for(;h>=0&&!(t[h]&1<<i);)n.sqrTo(o,g),p=o,o=g,g=p,--i<0&&(i=this.DB-1,--h)}return n.revert(o)}function bnGCD(t){var e=this.s<0?this.negate():this.clone(),r=t.s<0?t.negate():t.clone();if(e.compareTo(r)<0){var n=e;e=r,r=n}var i=e.getLowestSetBit(),o=r.getLowestSetBit();if(o<0)return e;for(i<o&&(o=i),o>0&&(e.rShiftTo(o,e),r.rShiftTo(o,r));e.signum()>0;)(i=e.getLowestSetBit())>0&&e.rShiftTo(i,e),(i=r.getLowestSetBit())>0&&r.rShiftTo(i,r),e.compareTo(r)>=0?(e.subTo(r,e),e.rShiftTo(1,e)):(r.subTo(e,r),r.rShiftTo(1,r));return o>0&&r.lShiftTo(o,r),r}function bnpModInt(t){if(t<=0)return 0;var e=this.DV%t,r=this.s<0?t-1:0;if(this.t>0)if(0==e)r=this[0]%t;else for(var n=this.t-1;n>=0;--n)r=(e*r+this[n])%t;return r}function bnModInverse(t){var e=t.isEven();if(this.isEven()&&e||0==t.signum())return BigInteger.ZERO;for(var r=t.clone(),n=this.clone(),i=nbv(1),o=nbv(0),a=nbv(0),s=nbv(1);0!=r.signum();){for(;r.isEven();)r.rShiftTo(1,r),e?(i.isEven()&&o.isEven()||(i.addTo(this,i),o.subTo(t,o)),i.rShiftTo(1,i)):o.isEven()||o.subTo(t,o),o.rShiftTo(1,o);for(;n.isEven();)n.rShiftTo(1,n),e?(a.isEven()&&s.isEven()||(a.addTo(this,a),s.subTo(t,s)),a.rShiftTo(1,a)):s.isEven()||s.subTo(t,s),s.rShiftTo(1,s);r.compareTo(n)>=0?(r.subTo(n,r),e&&i.subTo(a,i),o.subTo(s,o)):(n.subTo(r,n),e&&a.subTo(i,a),s.subTo(o,s))}return 0!=n.compareTo(BigInteger.ONE)?BigInteger.ZERO:s.compareTo(t)>=0?s.subtract(t):s.signum()<0?(s.addTo(t,s),s.signum()<0?s.add(t):s):s}Classic.prototype.convert=cConvert,Classic.prototype.revert=cRevert,Classic.prototype.reduce=cReduce,Classic.prototype.mulTo=cMulTo,Classic.prototype.sqrTo=cSqrTo,Montgomery.prototype.convert=montConvert,Montgomery.prototype.revert=montRevert,Montgomery.prototype.reduce=montReduce,Montgomery.prototype.mulTo=montMulTo,Montgomery.prototype.sqrTo=montSqrTo,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,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,BigInteger.ZERO=nbv(0),BigInteger.ONE=nbv(1),NullExp.prototype.convert=nNop,NullExp.prototype.revert=nNop,NullExp.prototype.mulTo=nMulTo,NullExp.prototype.sqrTo=nSqrTo,Barrett.prototype.convert=barrettConvert,Barrett.prototype.revert=barrettRevert,Barrett.prototype.reduce=barrettReduce,Barrett.prototype.mulTo=barrettMulTo,Barrett.prototype.sqrTo=barrettSqrTo;var lowprimes=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997],lplim=(1<<26)/lowprimes[lowprimes.length-1];function bnIsProbablePrime(t){var e,r=this.abs();if(1==r.t&&r[0]<=lowprimes[lowprimes.length-1]){for(e=0;e<lowprimes.length;++e)if(r[0]==lowprimes[e])return!0;return!1}if(r.isEven())return!1;for(e=1;e<lowprimes.length;){for(var n=lowprimes[e],i=e+1;i<lowprimes.length&&n<lplim;)n*=lowprimes[i++];for(n=r.modInt(n);e<i;)if(n%lowprimes[e++]==0)return!1}return r.millerRabin(t)}function bnpMillerRabin(t){var e=this.subtract(BigInteger.ONE),r=e.getLowestSetBit();if(r<=0)return!1;var n=e.shiftRight(r);(t=t+1>>1)>lowprimes.length&&(t=lowprimes.length);for(var i=nbi(),o=0;o<t;++o){i.fromInt(lowprimes[Math.floor(Math.random()*lowprimes.length)]);var a=i.modPow(n,this);if(0!=a.compareTo(BigInteger.ONE)&&0!=a.compareTo(e)){for(var s=1;s++<r&&0!=a.compareTo(e);)if(0==(a=a.modPowInt(2,this)).compareTo(BigInteger.ONE))return!1;if(0!=a.compareTo(e))return!1}}return!0}function Arcfour(){this.i=0,this.j=0,this.S=new Array}function ARC4init(t){var e,r,n;for(e=0;e<256;++e)this.S[e]=e;for(r=0,e=0;e<256;++e)r=r+this.S[e]+t[e%t.length]&255,n=this.S[e],this.S[e]=this.S[r],this.S[r]=n;this.i=0,this.j=0}function ARC4next(){var t;return this.i=this.i+1&255,this.j=this.j+this.S[this.i]&255,t=this.S[this.i],this.S[this.i]=this.S[this.j],this.S[this.j]=t,this.S[t+this.S[this.i]&255]}function prng_newstate(){return new Arcfour}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,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.prototype.square=bnSquare,Arcfour.prototype.init=ARC4init,Arcfour.prototype.next=ARC4next;var rng_state,rng_pool,rng_pptr,rng_psize=256;function rng_seed_int(t){rng_pool[rng_pptr++]^=255&t,rng_pool[rng_pptr++]^=t>>8&255,rng_pool[rng_pptr++]^=t>>16&255,rng_pool[rng_pptr++]^=t>>24&255,rng_pptr>=rng_psize&&(rng_pptr-=rng_psize)}function rng_seed_time(){rng_seed_int((new Date).getTime())}if(null==rng_pool){var t;if(rng_pool=new Array,rng_pptr=0,window.crypto&&window.crypto.getRandomValues){var ua=new Uint8Array(32);for(window.crypto.getRandomValues(ua),t=0;t<32;++t)rng_pool[rng_pptr++]=ua[t]}if("Netscape"==navigator.appName&&navigator.appVersion<"5"&&window.crypto){var z=window.crypto.random(32);for(t=0;t<z.length;++t)rng_pool[rng_pptr++]=255&z.charCodeAt(t)}for(;rng_pptr<rng_psize;)t=Math.floor(65536*Math.random()),rng_pool[rng_pptr++]=t>>>8,rng_pool[rng_pptr++]=255&t;rng_pptr=0,rng_seed_time()}function rng_get_byte(){if(null==rng_state){for(rng_seed_time(),(rng_state=prng_newstate()).init(rng_pool),rng_pptr=0;rng_pptr<rng_pool.length;++rng_pptr)rng_pool[rng_pptr]=0;rng_pptr=0}return rng_state.next()}function rng_get_bytes(t){var e;for(e=0;e<t.length;++e)t[e]=rng_get_byte()}function SecureRandom(){}SecureRandom.prototype.nextBytes=rng_get_bytes;var RSAPublicKey=function(t,e){this.modulus=new BigInteger(Hex.encode(t),16),this.encryptionExponent=new BigInteger(Hex.encode(e),16)},UTF8={encode:function(t){t=t.replace(/\r\n/g,"\n");for(var e="",r=0;r<t.length;r++){var n=t.charCodeAt(r);n<128?e+=String.fromCharCode(n):n>127&&n<2048?(e+=String.fromCharCode(n>>6|192),e+=String.fromCharCode(63&n|128)):(e+=String.fromCharCode(n>>12|224),e+=String.fromCharCode(n>>6&63|128),e+=String.fromCharCode(63&n|128))}return e},decode:function(t){for(var e="",r=0,n=$c1=$c2=0;r<t.length;)(n=t.charCodeAt(r))<128?(e+=String.fromCharCode(n),r++):n>191&&n<224?($c2=t.charCodeAt(r+1),e+=String.fromCharCode((31&n)<<6|63&$c2),r+=2):($c2=t.charCodeAt(r+1),$c3=t.charCodeAt(r+2),e+=String.fromCharCode((15&n)<<12|(63&$c2)<<6|63&$c3),r+=3);return e}},Base64={base64:"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=",encode:function(t){if(!t)return!1;var e,r,n,i,o,a,s,l="",c=0;do{i=(e=t.charCodeAt(c++))>>2,o=(3&e)<<4|(r=t.charCodeAt(c++))>>4,a=(15&r)<<2|(n=t.charCodeAt(c++))>>6,s=63&n,isNaN(r)?a=s=64:isNaN(n)&&(s=64),l+=this.base64.charAt(i)+this.base64.charAt(o)+this.base64.charAt(a)+this.base64.charAt(s)}while(c<t.length);return l},decode:function(t){if(!t)return!1;t=t.replace(/[^A-Za-z0-9\+\/\=]/g,"");var e,r,n,i,o="",a=0;do{e=this.base64.indexOf(t.charAt(a++)),r=this.base64.indexOf(t.charAt(a++)),n=this.base64.indexOf(t.charAt(a++)),i=this.base64.indexOf(t.charAt(a++)),o+=String.fromCharCode(e<<2|r>>4),64!=n&&(o+=String.fromCharCode((15&r)<<4|n>>2)),64!=i&&(o+=String.fromCharCode((3&n)<<6|i))}while(a<t.length);return o}},Hex={hex:"0123456789abcdef",encode:function(t){if(!t)return!1;var e,r="",n=0;do{e=t.charCodeAt(n++),r+=this.hex.charAt(e>>4&15)+this.hex.charAt(15&e)}while(n<t.length);return r},decode:function(t){if(!t)return!1;t=t.replace(/[^0-9abcdef]/g,"");var e="",r=0;do{e+=String.fromCharCode(this.hex.indexOf(t.charAt(r++))<<4&240|15&this.hex.indexOf(t.charAt(r++)))}while(r<t.length);return e}},ASN1Data=function(t){this.error=!1,this.parse=function(t){if(!t)return this.error=!0,null;for(var e=[];t.length>0;){var r=t.charCodeAt(0);t=t.substr(1);var n=0;if(5==(31&r))t=t.substr(1);else if(128&t.charCodeAt(0)){var i=127&t.charCodeAt(0);if(t=t.substr(1),i>0&&(n=t.charCodeAt(0)),i>1&&(n=n<<8|t.charCodeAt(1)),i>2)return this.error=!0,null;t=t.substr(i)}else n=t.charCodeAt(0),t=t.substr(1);var o="";if(n){if(n>t.length)return this.error=!0,null;o=t.substr(0,n),t=t.substr(n)}32&r?e.push(this.parse(o)):e.push(this.value(128&r?4:31&r,o))}return e},this.value=function(t,e){if(1==t)return!!e;if(2==t)return e;if(3==t)return this.parse(e.substr(1));if(5==t)return null;if(6==t){var r=[],n=e.charCodeAt(0);r.push(Math.floor(n/40)),r.push(n-40*r[0]);var i,o=[],a=0;for(i=1;i<e.length;i++){var s=e.charCodeAt(i);if(o.push(127&s),128&s)a++;else{var l,c=0;for(l=0;l<o.length;l++)c+=o[l]*Math.pow(128,a--);r.push(c),a=0,o=[]}}return r.join(".")}return null},this.data=this.parse(t)},RSA={getPublicKey:function(t){return!(t.length<50)&&("-----BEGIN PUBLIC KEY-----"==t.substr(0,26)&&("-----END PUBLIC KEY-----"==(t=t.substr(26)).substr(t.length-24)&&(t=t.substr(0,t.length-24),!(t=new ASN1Data(Base64.decode(t))).error&&("1.2.840.113549.1.1.1"==(t=t.data)[0][0][0]&&new RSAPublicKey(t[0][1][0][0],t[0][1][0][1])))))},encrypt:function(t,e){if(!e)return!1;var r=e.modulus.bitLength()+7>>3;if(!(t=this.pkcs1pad2(t,r)))return!1;if(!(t=t.modPowInt(e.encryptionExponent,e.modulus)))return!1;for(t=t.toString(16);t.length<2*r;)t="0"+t;return Base64.encode(Hex.decode(t))},decrypt:function(t,e){if(!e)return!1;for(t=Hex.encode(Base64.decode(t)).toString(16);"0"==t[0];)t=t.replace("0","");if(!(t=(t=new BigInteger(t,16)).modPowInt(e.encryptionExponent,e.modulus)))return!1;var r=e.modulus.bitLength()+7>>3;return t=this.pkcs1unpad2(t,r)},pkcs1pad2:function(t,e){if(e<t.length+11)return null;for(var r=new Array,n=t.length-1;n>=0&&e>0;){var i=t.charCodeAt(n--);i<128?r[--e]=i:i>127&&i<2048?(r[--e]=63&i|128,r[--e]=i>>6|192):(r[--e]=63&i|128,r[--e]=i>>6&63|128,r[--e]=i>>12|224)}r[--e]=0;for(var o=new SecureRandom,a=new Array;e>2;){for(a[0]=0;0==a[0];)o.nextBytes(a);r[--e]=a[0]}return r[--e]=2,r[--e]=0,new BigInteger(r)},pkcs1unpad2:function(t,e){for(var r=t.toByteArray(),n=0;n<r.length&&0==r[n];)++n;for(++n;0!=r[n];)if(++n>=r.length)return null;for(var i="";++n<r.length;){var o=255&r[n];o<128?i+=String.fromCharCode(o):o>191&&o<224?(i+=String.fromCharCode((31&o)<<6|63&r[n+1]),++n):(i+=String.fromCharCode((15&o)<<12|(63&r[n+1])<<6|63&r[n+2]),n+=2)}return i}};!function(t){"use strict";t.__InputSecurity={rsaDecrypt:function(t){return RSA.decrypt(t,__InputSecurity.getPublicRSA())},rsaEncrypt:function(t){return RSA.encrypt(t,__InputSecurity.getPublicRSA())},getPublicRSA:function(){return RSA.getPublicKey(t.__pbkey?t.__pbkey:"-----BEGIN PUBLIC KEY-----MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBAPJwwNa//eaQYxkNsAODohg38azVtalEh7Lw4wxlBrbDONgYaebgscpjPRloeL0kj4aLI462lcQGVAxhyh8JijsCAwEAAQ==-----END PUBLIC KEY-----")},processSecuredData:function(t){if(t&&t.__maskedData){for(var e=t.__maskedData.split("__==__"),r="",n=0;n<e.length;n++)e[n]&&(r+=__InputSecurity.rsaDecrypt(e[n]));return 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