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Filename : BigInteger.min.js
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var bigInt=function(t){"use strict";var e=1e7,r=9007199254740992,o=f(r),n="0123456789abcdefghijklmnopqrstuvwxyz",i="function"==typeof BigInt;function u(t,e,r,o){return void 0===t?u[0]:void 0!==e&&(10!=+e||r)?_(t,e,r,o):K(t)}function p(t,e){this.value=t,this.sign=e,this.isSmall=!1}function a(t){this.value=t,this.sign=t<0,this.isSmall=!0}function s(t){this.value=t}function l(t){return-r<t&&t<r}function f(t){return t<1e7?[t]:t<1e14?[t%1e7,Math.floor(t/1e7)]:[t%1e7,Math.floor(t/1e7)%1e7,Math.floor(t/1e14)]}function v(t){h(t);var r=t.length;if(r<4&&A(t,o)<0)switch(r){case 0:return 0;case 1:return t[0];case 2:return t[0]+t[1]*e;default:return t[0]+(t[1]+t[2]*e)*e}return t}function h(t){for(var e=t.length;0===t[--e];);t.length=e+1}function y(t){for(var e=new Array(t),r=-1;++r<t;)e[r]=0;return e}function g(t){return t>0?Math.floor(t):Math.ceil(t)}function c(t,r){var o,n,i=t.length,u=r.length,p=new Array(i),a=0,s=e;for(n=0;n<u;n++)a=(o=t[n]+r[n]+a)>=s?1:0,p[n]=o-a*s;for(;n<i;)a=(o=t[n]+a)===s?1:0,p[n++]=o-a*s;return a>0&&p.push(a),p}function m(t,e){return t.length>=e.length?c(t,e):c(e,t)}function d(t,r){var o,n,i=t.length,u=new Array(i),p=e;for(n=0;n<i;n++)o=t[n]-p+r,r=Math.floor(o/p),u[n]=o-r*p,r+=1;for(;r>0;)u[n++]=r%p,r=Math.floor(r/p);return u}function b(t,r){var o,n,i=t.length,u=r.length,p=new Array(i),a=0,s=e;for(o=0;o<u;o++)(n=t[o]-a-r[o])<0?(n+=s,a=1):a=0,p[o]=n;for(o=u;o<i;o++){if(!((n=t[o]-a)<0)){p[o++]=n;break}n+=s,p[o]=n}for(;o<i;o++)p[o]=t[o];return h(p),p}function w(t,r,o){var n,i,u=t.length,s=new Array(u),l=-r,f=e;for(n=0;n<u;n++)i=t[n]+l,l=Math.floor(i/f),i%=f,s[n]=i<0?i+f:i;return"number"==typeof(s=v(s))?(o&&(s=-s),new a(s)):new p(s,o)}function S(t,r){var o,n,i,u,p=t.length,a=r.length,s=y(p+a),l=e;for(i=0;i<p;++i){u=t[i];for(var f=0;f<a;++f)o=u*r[f]+s[i+f],n=Math.floor(o/l),s[i+f]=o-n*l,s[i+f+1]+=n}return h(s),s}function I(t,r){var o,n,i=t.length,u=new Array(i),p=e,a=0;for(n=0;n<i;n++)o=t[n]*r+a,a=Math.floor(o/p),u[n]=o-a*p;for(;a>0;)u[n++]=a%p,a=Math.floor(a/p);return u}function q(t,e){for(var r=[];e-- >0;)r.push(0);return r.concat(t)}function M(t,e){var r=Math.max(t.length,e.length);if(r<=30)return S(t,e);r=Math.ceil(r/2);var o=t.slice(r),n=t.slice(0,r),i=e.slice(r),u=e.slice(0,r),p=M(n,u),a=M(o,i),s=M(m(n,o),m(u,i)),l=m(m(p,q(b(b(s,p),a),r)),q(a,2*r));return h(l),l}function N(t,r,o){return new p(t<e?I(r,t):S(r,f(t)),o)}function E(t){var r,o,n,i,u=t.length,p=y(u+u),a=e;for(n=0;n<u;n++){o=0-(i=t[n])*i;for(var s=n;s<u;s++)r=i*t[s]*2+p[n+s]+o,o=Math.floor(r/a),p[n+s]=r-o*a;p[n+u]=o}return h(p),p}function O(t,e){var r,o,n,i,u=t.length,p=y(u);for(n=0,r=u-1;r>=0;--r)n=(i=1e7*n+t[r])-(o=g(i/e))*e,p[r]=0|o;return[p,0|n]}function B(t,r){var o,n=K(r);if(i)return[new s(t.value/n.value),new s(t.value%n.value)];var l,c=t.value,m=n.value;if(0===m)throw new Error("Cannot divide by zero");if(t.isSmall)return n.isSmall?[new a(g(c/m)),new a(c%m)]:[u[0],t];if(n.isSmall){if(1===m)return[t,u[0]];if(-1==m)return[t.negate(),u[0]];var d=Math.abs(m);if(d<e){l=v((o=O(c,d))[0]);var w=o[1];return t.sign&&(w=-w),"number"==typeof l?(t.sign!==n.sign&&(l=-l),[new a(l),new a(w)]):[new p(l,t.sign!==n.sign),new a(w)]}m=f(d)}var S=A(c,m);if(-1===S)return[u[0],t];if(0===S)return[u[t.sign===n.sign?1:-1],u[0]];o=c.length+m.length<=200?function(t,r){var o,n,i,u,p,a,s,l=t.length,f=r.length,h=e,g=y(r.length),c=r[f-1],m=Math.ceil(h/(2*c)),d=I(t,m),b=I(r,m);for(d.length<=l&&d.push(0),b.push(0),c=b[f-1],n=l-f;n>=0;n--){for(o=h-1,d[n+f]!==c&&(o=Math.floor((d[n+f]*h+d[n+f-1])/c)),i=0,u=0,a=b.length,p=0;p<a;p++)i+=o*b[p],s=Math.floor(i/h),u+=d[n+p]-(i-s*h),i=s,u<0?(d[n+p]=u+h,u=-1):(d[n+p]=u,u=0);for(;0!==u;){for(o-=1,i=0,p=0;p<a;p++)(i+=d[n+p]-h+b[p])<0?(d[n+p]=i+h,i=0):(d[n+p]=i,i=1);u+=i}g[n]=o}return d=O(d,m)[0],[v(g),v(d)]}(c,m):function(t,r){for(var o,n,i,u,p,a=t.length,s=r.length,l=[],f=[],y=e;a;)if(f.unshift(t[--a]),h(f),A(f,r)<0)l.push(0);else{i=f[(n=f.length)-1]*y+f[n-2],u=r[s-1]*y+r[s-2],n>s&&(i=(i+1)*y),o=Math.ceil(i/u);do{if(A(p=I(r,o),f)<=0)break;o--}while(o);l.push(o),f=b(f,p)}return l.reverse(),[v(l),v(f)]}(c,m),l=o[0];var q=t.sign!==n.sign,M=o[1],N=t.sign;return"number"==typeof l?(q&&(l=-l),l=new a(l)):l=new p(l,q),"number"==typeof M?(N&&(M=-M),M=new a(M)):M=new p(M,N),[l,M]}function A(t,e){if(t.length!==e.length)return t.length>e.length?1:-1;for(var r=t.length-1;r>=0;r--)if(t[r]!==e[r])return t[r]>e[r]?1:-1;return 0}function P(t){var e=t.abs();return!e.isUnit()&&(!!(e.equals(2)||e.equals(3)||e.equals(5))||!(e.isEven()||e.isDivisibleBy(3)||e.isDivisibleBy(5))&&(!!e.lesser(49)||void 0))}function Z(t,e){for(var r,o,n,i=t.prev(),u=i,p=0;u.isEven();)u=u.divide(2),p++;t:for(o=0;o<e.length;o++)if(!t.lesser(e[o])&&!(n=bigInt(e[o]).modPow(u,t)).isUnit()&&!n.equals(i)){for(r=p-1;0!=r;r--){if((n=n.square().mod(t)).isUnit())return!1;if(n.equals(i))continue t}return!1}return!0}p.prototype=Object.create(u.prototype),a.prototype=Object.create(u.prototype),s.prototype=Object.create(u.prototype),p.prototype.add=function(t){var e=K(t);if(this.sign!==e.sign)return this.subtract(e.negate());var r=this.value,o=e.value;return e.isSmall?new p(d(r,Math.abs(o)),this.sign):new p(m(r,o),this.sign)},p.prototype.plus=p.prototype.add,a.prototype.add=function(t){var e=K(t),r=this.value;if(r<0!==e.sign)return this.subtract(e.negate());var o=e.value;if(e.isSmall){if(l(r+o))return new a(r+o);o=f(Math.abs(o))}return new p(d(o,Math.abs(r)),r<0)},a.prototype.plus=a.prototype.add,s.prototype.add=function(t){return new s(this.value+K(t).value)},s.prototype.plus=s.prototype.add,p.prototype.subtract=function(t){var e=K(t);if(this.sign!==e.sign)return this.add(e.negate());var r=this.value,o=e.value;return e.isSmall?w(r,Math.abs(o),this.sign):function(t,e,r){var o;return A(t,e)>=0?o=b(t,e):(o=b(e,t),r=!r),"number"==typeof(o=v(o))?(r&&(o=-o),new a(o)):new p(o,r)}(r,o,this.sign)},p.prototype.minus=p.prototype.subtract,a.prototype.subtract=function(t){var e=K(t),r=this.value;if(r<0!==e.sign)return this.add(e.negate());var o=e.value;return e.isSmall?new a(r-o):w(o,Math.abs(r),r>=0)},a.prototype.minus=a.prototype.subtract,s.prototype.subtract=function(t){return new s(this.value-K(t).value)},s.prototype.minus=s.prototype.subtract,p.prototype.negate=function(){return new p(this.value,!this.sign)},a.prototype.negate=function(){var t=this.sign,e=new a(-this.value);return e.sign=!t,e},s.prototype.negate=function(){return new s(-this.value)},p.prototype.abs=function(){return new p(this.value,!1)},a.prototype.abs=function(){return new a(Math.abs(this.value))},s.prototype.abs=function(){return new s(this.value>=0?this.value:-this.value)},p.prototype.multiply=function(t){var r,o,n,i=K(t),a=this.value,s=i.value,l=this.sign!==i.sign;if(i.isSmall){if(0===s)return u[0];if(1===s)return this;if(-1===s)return this.negate();if((r=Math.abs(s))<e)return new p(I(a,r),l);s=f(r)}return o=a.length,n=s.length,new p(-.012*o-.012*n+15e-6*o*n>0?M(a,s):S(a,s),l)},p.prototype.times=p.prototype.multiply,a.prototype._multiplyBySmall=function(t){return l(t.value*this.value)?new a(t.value*this.value):N(Math.abs(t.value),f(Math.abs(this.value)),this.sign!==t.sign)},p.prototype._multiplyBySmall=function(t){return 0===t.value?u[0]:1===t.value?this:-1===t.value?this.negate():N(Math.abs(t.value),this.value,this.sign!==t.sign)},a.prototype.multiply=function(t){return K(t)._multiplyBySmall(this)},a.prototype.times=a.prototype.multiply,s.prototype.multiply=function(t){return new s(this.value*K(t).value)},s.prototype.times=s.prototype.multiply,p.prototype.square=function(){return new p(E(this.value),!1)},a.prototype.square=function(){var t=this.value*this.value;return l(t)?new a(t):new p(E(f(Math.abs(this.value))),!1)},s.prototype.square=function(t){return new s(this.value*this.value)},p.prototype.divmod=function(t){var e=B(this,t);return{quotient:e[0],remainder:e[1]}},s.prototype.divmod=a.prototype.divmod=p.prototype.divmod,p.prototype.divide=function(t){return B(this,t)[0]},s.prototype.over=s.prototype.divide=function(t){return new s(this.value/K(t).value)},a.prototype.over=a.prototype.divide=p.prototype.over=p.prototype.divide,p.prototype.mod=function(t){return B(this,t)[1]},s.prototype.mod=s.prototype.remainder=function(t){return new s(this.value%K(t).value)},a.prototype.remainder=a.prototype.mod=p.prototype.remainder=p.prototype.mod,p.prototype.pow=function(t){var e,r,o,n=K(t),i=this.value,p=n.value;if(0===p)return u[1];if(0===i)return u[0];if(1===i)return u[1];if(-1===i)return n.isEven()?u[1]:u[-1];if(n.sign)return u[0];if(!n.isSmall)throw new Error("The exponent "+n.toString()+" is too large.");if(this.isSmall&&l(e=Math.pow(i,p)))return new a(g(e));for(r=this,o=u[1];!0&p&&(o=o.times(r),--p),0!==p;)p/=2,r=r.square();return o},a.prototype.pow=p.prototype.pow,s.prototype.pow=function(t){var e=K(t),r=this.value,o=e.value,n=BigInt(0),i=BigInt(1),p=BigInt(2);if(o===n)return u[1];if(r===n)return u[0];if(r===i)return u[1];if(r===BigInt(-1))return e.isEven()?u[1]:u[-1];if(e.isNegative())return new s(n);for(var a=this,l=u[1];(o&i)===i&&(l=l.times(a),--o),o!==n;)o/=p,a=a.square();return l},p.prototype.modPow=function(t,e){if(t=K(t),(e=K(e)).isZero())throw new Error("Cannot take modPow with modulus 0");var r=u[1],o=this.mod(e);for(t.isNegative()&&(t=t.multiply(u[-1]),o=o.modInv(e));t.isPositive();){if(o.isZero())return u[0];t.isOdd()&&(r=r.multiply(o).mod(e)),t=t.divide(2),o=o.square().mod(e)}return r},s.prototype.modPow=a.prototype.modPow=p.prototype.modPow,p.prototype.compareAbs=function(t){var e=K(t),r=this.value,o=e.value;return e.isSmall?1:A(r,o)},a.prototype.compareAbs=function(t){var e=K(t),r=Math.abs(this.value),o=e.value;return e.isSmall?r===(o=Math.abs(o))?0:r>o?1:-1:-1},s.prototype.compareAbs=function(t){var e=this.value,r=K(t).value;return(e=e>=0?e:-e)===(r=r>=0?r:-r)?0:e>r?1:-1},p.prototype.compare=function(t){if(t===1/0)return-1;if(t===-1/0)return 1;var e=K(t),r=this.value,o=e.value;return this.sign!==e.sign?e.sign?1:-1:e.isSmall?this.sign?-1:1:A(r,o)*(this.sign?-1:1)},p.prototype.compareTo=p.prototype.compare,a.prototype.compare=function(t){if(t===1/0)return-1;if(t===-1/0)return 1;var e=K(t),r=this.value,o=e.value;return e.isSmall?r==o?0:r>o?1:-1:r<0!==e.sign?r<0?-1:1:r<0?1:-1},a.prototype.compareTo=a.prototype.compare,s.prototype.compare=function(t){if(t===1/0)return-1;if(t===-1/0)return 1;var e=this.value,r=K(t).value;return e===r?0:e>r?1:-1},s.prototype.compareTo=s.prototype.compare,p.prototype.equals=function(t){return 0===this.compare(t)},s.prototype.eq=s.prototype.equals=a.prototype.eq=a.prototype.equals=p.prototype.eq=p.prototype.equals,p.prototype.notEquals=function(t){return 0!==this.compare(t)},s.prototype.neq=s.prototype.notEquals=a.prototype.neq=a.prototype.notEquals=p.prototype.neq=p.prototype.notEquals,p.prototype.greater=function(t){return this.compare(t)>0},s.prototype.gt=s.prototype.greater=a.prototype.gt=a.prototype.greater=p.prototype.gt=p.prototype.greater,p.prototype.lesser=function(t){return this.compare(t)<0},s.prototype.lt=s.prototype.lesser=a.prototype.lt=a.prototype.lesser=p.prototype.lt=p.prototype.lesser,p.prototype.greaterOrEquals=function(t){return this.compare(t)>=0},s.prototype.geq=s.prototype.greaterOrEquals=a.prototype.geq=a.prototype.greaterOrEquals=p.prototype.geq=p.prototype.greaterOrEquals,p.prototype.lesserOrEquals=function(t){return this.compare(t)<=0},s.prototype.leq=s.prototype.lesserOrEquals=a.prototype.leq=a.prototype.lesserOrEquals=p.prototype.leq=p.prototype.lesserOrEquals,p.prototype.isEven=function(){return 0==(1&this.value[0])},a.prototype.isEven=function(){return 0==(1&this.value)},s.prototype.isEven=function(){return(this.value&BigInt(1))===BigInt(0)},p.prototype.isOdd=function(){return 1==(1&this.value[0])},a.prototype.isOdd=function(){return 1==(1&this.value)},s.prototype.isOdd=function(){return(this.value&BigInt(1))===BigInt(1)},p.prototype.isPositive=function(){return!this.sign},a.prototype.isPositive=function(){return this.value>0},s.prototype.isPositive=a.prototype.isPositive,p.prototype.isNegative=function(){return this.sign},a.prototype.isNegative=function(){return this.value<0},s.prototype.isNegative=a.prototype.isNegative,p.prototype.isUnit=function(){return!1},a.prototype.isUnit=function(){return 1===Math.abs(this.value)},s.prototype.isUnit=function(){return this.abs().value===BigInt(1)},p.prototype.isZero=function(){return!1},a.prototype.isZero=function(){return 0===this.value},s.prototype.isZero=function(){return this.value===BigInt(0)},p.prototype.isDivisibleBy=function(t){var e=K(t);return!e.isZero()&&(!!e.isUnit()||(0===e.compareAbs(2)?this.isEven():this.mod(e).isZero()))},s.prototype.isDivisibleBy=a.prototype.isDivisibleBy=p.prototype.isDivisibleBy,p.prototype.isPrime=function(e){var r=P(this);if(r!==t)return r;var o=this.abs(),n=o.bitLength();if(n<=64)return Z(o,[2,3,5,7,11,13,17,19,23,29,31,37]);for(var i=Math.log(2)*n.toJSNumber(),u=Math.ceil(!0===e?2*Math.pow(i,2):i),p=[],a=0;a<u;a++)p.push(bigInt(a+2));return Z(o,p)},s.prototype.isPrime=a.prototype.isPrime=p.prototype.isPrime,p.prototype.isProbablePrime=function(e,r){var o=P(this);if(o!==t)return o;for(var n=this.abs(),i=e===t?5:e,u=[],p=0;p<i;p++)u.push(bigInt.randBetween(2,n.minus(2),r));return Z(n,u)},s.prototype.isProbablePrime=a.prototype.isProbablePrime=p.prototype.isProbablePrime,p.prototype.modInv=function(t){for(var e,r,o,n=bigInt.zero,i=bigInt.one,u=K(t),p=this.abs();!p.isZero();)e=u.divide(p),r=n,o=u,n=i,u=p,i=r.subtract(e.multiply(i)),p=o.subtract(e.multiply(p));if(!u.isUnit())throw new Error(this.toString()+" and "+t.toString()+" are not co-prime");return-1===n.compare(0)&&(n=n.add(t)),this.isNegative()?n.negate():n},s.prototype.modInv=a.prototype.modInv=p.prototype.modInv,p.prototype.next=function(){var t=this.value;return this.sign?w(t,1,this.sign):new p(d(t,1),this.sign)},a.prototype.next=function(){var t=this.value;return t+1<r?new a(t+1):new p(o,!1)},s.prototype.next=function(){return new s(this.value+BigInt(1))},p.prototype.prev=function(){var t=this.value;return this.sign?new p(d(t,1),!0):w(t,1,this.sign)},a.prototype.prev=function(){var t=this.value;return t-1>-r?new a(t-1):new p(o,!0)},s.prototype.prev=function(){return new s(this.value-BigInt(1))};for(var 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