text: var bigInt=function(e){"use strict";function o(e,t){this.value=e,this.sign=t,this.isSmall=!1}function u(e){this.value=e,this.sign=e<0,this.isSmall=!0}function a(e){return-r<e&&e<r}function f(e){return e<1e7?[e]:e<1e14?[e%1e7,Math.floor(e/1e7)]:[e%1e7,Math.floor(e/1e7)%1e7,Math.floor(e/1e14)]}function l(e){c(e);var n=e.length;if(n<4&&O(e,i)<0)switch(n){case 0:return 0;case 1:return e[0];case 2:return e[0]+e[1]*t;default:return e[0]+(e[1]+e[2]*t)*t}return e}function c(e){var t=e.length;while(e[--t]===0);e.length=t+1}function h(e){var t=new Array(e),n=-1;while(++n<e)t[n]=0;return t}function p(e){return e>0?Math.floor(e):Math.ceil(e)}function d(e,n){var r=e.length,i=n.length,s=new Array(r),o=0,u=t,a,f;for(f=0;f<i;f++)a=e[f]+n[f]+o,o=a>=u?1:0,s[f]=a-o*u;while(f<r)a=e[f]+o,o=a===u?1:0,s[f++]=a-o*u;return o>0&&s.push(o),s}function v(e,t){return e.length>=t.length?d(e,t):d(t,e)}function m(e,n){var r=e.length,i=new Array(r),s=t,o,u;for(u=0;u<r;u++)o=e[u]-s+n,n=Math.floor(o/s),i[u]=o-n*s,n+=1;while(n>0)i[u++]=n%s,n=Math.floor(n/s);return i}function g(e,n){var r=e.length,i=n.length,s=new Array(r),o=0,u=t,a,f;for(a=0;a<i;a++)f=e[a]-o-n[a],f<0?(f+=u,o=1):o=0,s[a]=f;for(a=i;a<r;a++){f=e[a]-o;if(!(f<0)){s[a++]=f;break}f+=u,s[a]=f}for(;a<r;a++)s[a]=e[a];return c(s),s}function y(e,t,n){var r,i;return O(e,t)>=0?r=g(e,t):(r=g(t,e),n=!n),r=l(r),typeof r=="number"?(n&&(r=-r),new u(r)):new o(r,n)}function b(e,n,r){var i=e.length,s=new Array(i),a=-n,f=t,c,h;for(c=0;c<i;c++)h=e[c]+a,a=Math.floor(h/f),h%=f,s[c]=h<0?h+f:h;return s=l(s),typeof s=="number"?(r&&(s=-s),new u(s)):new o(s,r)}function w(e,n){var r=e.length,i=n.length,s=r+i,o=h(s),u=t,a,f,l,p,d;for(l=0;l<r;++l){p=e[l];for(var v=0;v<i;++v)d=n[v],a=p*d+o[l+v],f=Math.floor(a/u),o[l+v]=a-f*u,o[l+v+1]+=f}return c(o),o}function E(e,n){var r=e.length,i=new Array(r),s=t,o=0,u,a;for(a=0;a<r;a++)u=e[a]*n+o,o=Math.floor(u/s),i[a]=u-o*s;while(o>0)i[a++]=o%s,o=Math.floor(o/s);return i}function S(e,t){var n=[];while(t-->0)n.push(0);return n.concat(e)}function x(e,t){var n=Math.max(e.length,t.length);if(n<=400)return w(e,t);n=Math.ceil(n/2);var r=e.slice(n),i=e.slice(0,n),s=t.slice(n),o=t.slice(0,n),u=x(i,o),a=x(r,s),f=x(v(i,r),v(o,s));return v(v(u,S(g(g(f,u),a),n)),S(a,2*n))}function T(e,n,r){return e<t?new o(E(n,e),r):new o(w(n,f(e)),r)}function N(e){var n=e.length,r=h(n+n),i=t,s,o,u,a,f;for(u=0;u<n;u++){a=e[u];for(var l=0;l<n;l++)f=e[l],s=a*f+r[u+l],o=Math.floor(s/i),r[u+l]=s-o*i,r[u+l+1]+=o}return c(r),r}function C(e,n){var r=e.length,i=n.length,s=t,o=h(n.length),u=n[i-1],a=Math.ceil(s/(2*u)),f=E(e,a),c=E(n,a),p,d,v,m,g,y,b;f.length<=r&&f.push(0),c.push(0),u=c[i-1];for(d=r-i;d>=0;d--){p=s-1,p=Math.floor((f[d+i]*s+f[d+i-1])/u),v=0,m=0,y=c.length;for(g=0;g<y;g++)v+=p*c[g],b=Math.floor(v/s),m+=f[d+g]-(v-b*s),v=b,m<0?(f[d+g]=m+s,m=-1):(f[d+g]=m,m=0);while(m!==0){p-=1,v=0;for(g=0;g<y;g++)v+=f[d+g]-s+c[g],v<0?(f[d+g]=v+s,v=0):(f[d+g]=v,v=1);m+=v}o[d]=p}return f=L(f,a)[0],[l(o),l(f)]}function k(e,n){var r=e.length,i=n.length,s=[],o=[],u=t,a,f,c,h,p;while(r){o.unshift(e[--r]);if(O(o,n)<0){s.push(0);continue}f=o.length,c=o[f-1]*u+o[f-2],h=n[i-1]*u+n[i-2],f>i&&(c=(c+1)*u),a=Math.ceil(c/h);do{p=E(n,a);if(O(p,o)<=0)break;a--}while(a);s.push(a),o=g(o,p)}return s.reverse(),[l(s),l(o)]}function L(e,n){var r=e.length,i=h(r),s=t,o,u,a,f;a=0;for(o=r-1;o>=0;--o)f=a*s+e[o],u=p(f/n),a=f-u*n,i[o]=u|0;return[i,a|0]}function A(e,n){var r,i=$(n),s=e.value,a=i.value,c;if(a===0)throw new Error("Cannot divide by zero");if(e.isSmall)return i.isSmall?[new u(p(s/a)),new u(s%a)]:[J[0],e];if(i.isSmall){if(a===1)return[e,J[0]];if(a==-1)return[e.negate(),J[0]];var h=Math.abs(a);if(h<t){r=L(s,h),c=l(r[0]);var d=r[1];return e.sign&&(d=-d),typeof c=="number"?(e.sign!==i.sign&&(c=-c),[new u(c),new u(d)]):[new o(c,e.sign!==i.sign),new u(d)]}a=f(h)}var v=O(s,a);if(v===-1)return[J[0],e];if(v===0)return[J[e.sign===i.sign?1:-1],J[0]];s.length+a.length<=200?r=C(s,a):r=k(s,a),c=r[0];var m=e.sign!==i.sign,g=r[1],y=e.sign;return typeof c=="number"?(m&&(c=-c),c=new u(c)):c=new o(c,m),typeof g=="number"?(y&&(g=-g),g=new u(g)):g=new o(g,y),[c,g]}function O(e,t){if(e.length!==t.length)return e.length>t.length?1:-1;for(var n=e.length-1;n>=0;n--)if(e[n]!==t[n])return e[n]>t[n]?1:-1;return 0}function M(e){var t=e.abs();if(t.isUnit())return!1;if(t.equals(2)||t.equals(3)||t.equals(5))return!0;if(t.isEven()||t.isDivisibleBy(3)||t.isDivisibleBy(5))return!1;if(t.lesser(25))return!0}function H(e){return(typeof e=="number"||typeof e=="string")&&+Math.abs(e)<=t||e instanceof o&&e.value.length<=1}function B(e,t,n){t=$(t);var r=e.isNegative(),i=t.isNegative(),s=r?e.not():e,o=i?t.not():t,u=[],a=[],f=!1,l=!1;while(!f||!l)s.isZero()?(f=!0,u.push(r?1:0)):r?u.push(s.isEven()?1:0):u.push(s.isEven()?0:1),o.isZero()?(l=!0,a.push(i?1:0)):i?a.push(o.isEven()?1:0):a.push(o.isEven()?0:1),s=s.over(2),o=o.over(2);var c=[];for(var h=0;h<u.length;h++)c.push(n(u[h],a[h]));var p=bigInt(c.pop()).negate().times(bigInt(2).pow(c.length));while(c.length)p=p.add(bigInt(c.pop()).times(bigInt(2).pow(c.length)));return p}function j(e,t){return e=$(e),t=$(t),e.greater(t)?e:t}function F(e,t){return e=$(e),t=$(t),e.lesser(t)?e:t}function I(e,t){return e=$(e).abs(),t=$(t).abs(),e.equals(t)?e:e.isZero()?t:t.isZero()?e:e.isEven()?t.isOdd()?I(e.divide(2),t):I(e.divide(2),t.divide(2)).multiply(2):t.isEven()?I(e,t.divide(2)):e.greater(t)?I(e.subtract(t).divide(2),t):I(t.subtract(e).divide(2),e)}function q(e,t){return e=$(e).abs(),t=$(t).abs(),e.multiply(t).divide(I(e,t))}function R(e,n){e=$(e),n=$(n);var r=F(e,n),i=j(e,n),s=i.subtract(r);if(s.isSmall)return r.add(Math.round(Math.random()*s));var u=s.value.length-1,a=[],f=!0;for(var c=u;c>=0;c--){var h=f?s.value[c]:t,d=p(Math.random()*h);a.unshift(d),d<h&&(f=!1)}return a=l(a),r.add(new o(a,!1,typeof a=="number"))}function z(e){var t=e.value;return typeof t=="number"&&(t=[t]),t.length===1&&t[0]<=36?"0123456789abcdefghijklmnopqrstuvwxyz".charAt(t[0]):"<"+t+">"}function W(e,t){t=bigInt(t);if(t.isZero()){if(e.isZero())return"0";throw new Error("Cannot convert nonzero numbers to base 0.")}if(t.equals(-1))return e.isZero()?"0":e.isNegative()?(new Array(1-e)).join("10"):"1"+(new Array(+e)).join("01");var n="";e.isNegative()&&t.isPositive()&&(n="-",e=e.abs());if(t.equals(1))return e.isZero()?"0":n+(new Array(+e+1)).join(1);var r=[],i=e,s;while(i.isNegative()||i.compareAbs(t)>=0){s=i.divmod(t),i=s.quotient;var o=s.remainder;o.isNegative()&&(o=t.minus(o).abs(),i=i.next()),r.push(z(o))}return r.push(z(i)),n+r.reverse().join("")}function X(e){if(a(+e)){var t=+e;if(t===p(t))return new u(t);throw"Invalid integer: "+e}var r=e[0]==="-";r&&(e=e.slice(1));var i=e.split(/e/i);if(i.length>2)throw new Error("Invalid integer: "+f.join("e"));if(i.length===2){var s=i[1];s[0]==="+"&&(s=s.slice(1)),s=+s;if(s!==p(s)||!a(s))throw new Error("Invalid integer: "+s+" is not a valid exponent.");var f=i[0],l=f.indexOf(".");l>=0&&(s-=f.length-l,f=f.slice(0,l)+f.slice(l+1));if(s<0)throw new Error("Cannot include negative exponent part for integers");f+=(new Array(s+1)).join("0"),e=f}var h=/^([0-9][0-9]*)$/.test(e);if(!h)throw new Error("Invalid integer: "+e);var d=[],v=e.length,m=n,g=v-m;while(v>0)d.push(+e.slice(g,v)),g-=m,g<0&&(g=0),v-=m;return c(d),new o(d,r)}function V(e){return a(e)?new u(e):X(e.toString())}function $(e){return typeof e=="number"?V(e):typeof e=="string"?X(e):e}var t=1e7,n=7,r=9007199254740992,i=f(r),s=Math.log(r);o.prototype.add=function(e){var t,n=$(e);if(this.sign!==n.sign)return this.subtract(n.negate());var r=this.value,i=n.value;return n.isSmall?new o(m(r,Math.abs(i)),this.sign):new o(v(r,i),this.sign)},o.prototype.plus=o.prototype.add,u.prototype.add=function(e){var t=$(e),n=this.value;if(n<0!==t.sign)return this.subtract(t.negate());var r=t.value;if(t.isSmall){if(a(n+r))return new u(n+r);r=f(Math.abs(r))}return new o(m(r,Math.abs(n)),n<0)},u.prototype.plus=u.prototype.add,o.prototype.subtract=function(e){var t=$(e);if(this.sign!==t.sign)return this.add(t.negate());var n=this.value,r=t.value;return t.isSmall?b(n,Math.abs(r),this.sign):y(n,r,this.sign)},o.prototype.minus=o.prototype.subtract,u.prototype.subtract=function(e){var t=$(e),n=this.value;if(n<0!==t.sign)return this.add(t.negate());var r=t.value;return t.isSmall?new u(n-r):b(r,Math.abs(n),n>=0)},u.prototype.minus=u.prototype.subtract,o.prototype.negate=function(){return new o(this.value,!this.sign)},u.prototype.negate=function(){var e=this.sign,t=new u(-this.value);return t.sign=!e,t},o.prototype.abs=function(){return new o(this.value,!1)},u.prototype.abs=function(){return new u(Math.abs(this.value))},o.prototype.multiply=function(e){var n,r=$(e),i=this.value,s=r.value,u=this.sign!==r.sign,a;if(r.isSmall){if(s===0)return J[0];if(s===1)return this;if(s===-1)return this.negate();a=Math.abs(s);if(a<t)return new o(E(i,a),u);s=f(a)}return i.length+s.length>4e3?new o(x(i,s),u):new o(w(i,s),u)},o.prototype.times=o.prototype.multiply,u.prototype._multiplyBySmall=function(e){return a(e.value*this.value)?new u(e.value*this.value):T(Math.abs(e.value),f(Math.abs(this.value)),this.sign!==e.sign)},o.prototype._multiplyBySmall=function(e){return e.value===0?J[0]:e.value===1?this:e.value===-1?this.negate():T(Math.abs(e.value),this.value,this.sign!==e.sign)},u.prototype.multiply=function(e){return $(e)._multiplyBySmall(this)},u.prototype.times=u.prototype.multiply,o.prototype.square=function(){return new o(N(this.value),!1)},u.prototype.square=function(){var e=this.value*this.value;return a(e)?new u(e):new o(N(f(Math.abs(this.value))),!1)},o.prototype.divmod=function(e){var t=A(this,e);return{quotient:t[0],remainder:t[1]}},u.prototype.divmod=o.prototype.divmod,o.prototype.divide=function(e){return A(this,e)[0]},u.prototype.over=u.prototype.divide=o.prototype.over=o.prototype.divide,o.prototype.mod=function(e){return A(this,e)[1]},u.prototype.remainder=u.prototype.mod=o.prototype.remainder=o.prototype.mod,o.prototype.pow=function(e){var t=$(e),n=this.value,r=t.value,i,s,o;if(r===0)return J[1];if(n===0)return J[0];if(n===1)return J[1];if(n===-1)return t.isEven()?J[1]:J[-1];if(t.sign)return J[0];if(!t.isSmall)throw new Error("The exponent "+t.toString()+" is too large.");if(this.isSmall&&a(i=Math.pow(n,r)))return new u(p(i));s=this,o=J[1];for(;;){r&!0&&(o=o.times(s),--r);if(r===0)break;r/=2,s=s.square()}return o},u.prototype.pow=o.prototype.pow,o.prototype.modPow=function(e,t){e=$(e),t=$(t);if(t.isZero())throw new Error("Cannot take modPow with modulus 0");var n=J[1],r=this.mod(t);if(r.isZero())return J[0];while(e.isPositive())e.isOdd()&&(n=n.multiply(r).mod(t)),e=e.divide(2),r=r.square().mod(t);return n},u.prototype.modPow=o.prototype.modPow,o.prototype.compareAbs=function(e){var t=$(e),n=this.value,r=t.value;return t.isSmall?1:O(n,r)},u.prototype.compareAbs=function(e){var t=$(e),n=Math.abs(this.value),r=t.value;return t.isSmall?(r=Math.abs(r),n===r?0:n>r?1:-1):-1},o.prototype.compare=function(e){var t=$(e),n=this.value,r=t.value;return this.sign!==t.sign?t.sign?1:-1:t.isSmall?this.sign?-1:1:O(n,r)*(this.sign?-1:1)},o.prototype.compareTo=o.prototype.compare,u.prototype.compare=function(e){var t=$(e),n=this.value,r=t.value;return t.isSmall?n==r?0:n>r?1:-1:n<0!==t.sign?n<0?-1:1:n<0?1:-1},u.prototype.compareTo=u.prototype.compare,o.prototype.equals=function(e){return this.compare(e)===0},u.prototype.eq=u.prototype.equals=o.prototype.eq=o.prototype.equals,o.prototype.notEquals=function(e){return this.compare(e)!==0},u.prototype.neq=u.prototype.notEquals=o.prototype.neq=o.prototype.notEquals,o.prototype.greater=function(e){return this.compare(e)>0},u.prototype.gt=u.prototype.greater=o.prototype.gt=o.prototype.greater,o.prototype.lesser=function(e){return this.compare(e)<0},u.prototype.lt=u.prototype.lesser=o.prototype.lt=o.prototype.lesser,o.prototype.greaterOrEquals=function(e){return this.compare(e)>=0},u.prototype.geq=u.prototype.greaterOrEquals=o.prototype.geq=o.prototype.greaterOrEquals,o.prototype.lesserOrEquals=function(e){return this.compare(e)<=0},u.prototype.leq=u.prototype.lesserOrEquals=o.prototype.leq=o.prototype.lesserOrEquals,o.prototype.isEven=function(){return(this.value[0]&1)===0},u.prototype.isEven=function(){return(this.value&1)===0},o.prototype.isOdd=function(){return(this.value[0]&1)===1},u.prototype.isOdd=function(){return(this.value&1)===1},o.prototype.isPositive=function(){return!this.sign},u.prototype.isPositive=function(){return this.value>0},o.prototype.isNegative=function(){return this.sign},u.prototype.isNegative=function(){return this.value<0},o.prototype.isUnit=function(){return!1},u.prototype.isUnit=function(){return Math.abs(this.value)===1},o.prototype.isZero=function(){return!1},u.prototype.isZero=function(){return this.value===0},o.prototype.isDivisibleBy=function(e){var t=$(e),n=t.value;return n===0?!1:n===1?!0:n===2?this.isEven():this.mod(t).equals(J[0])},u.prototype.isDivisibleBy=o.prototype.isDivisibleBy,o.prototype.isPrime=function(){var t=M(this);if(t!==e)return t;var n=this.abs(),r=n.prev(),i=[2,3,5,7,11,13,17,19],s=r,o,u,a,f;while(s.isEven())s=s.divide(2);for(a=0;a<i.length;a++){f=bigInt(i[a]).modPow(s,n);if(f.equals(J[1])||f.equals(r))continue;for(u=!0,o=s;u&&o.lesser(r);o=o.multiply(2))f=f.square().mod(n),f.equals(r)&&(u=!1);if(u)return!1}return!0},u.prototype.isPrime=o.prototype.isPrime,o.prototype.isProbablePrime=function(t){var n=M(this);if(n!==e)return n;var r=this.abs(),i=t===e?5:t;for(var s=0;s<i;s++){var o=bigInt.randBetween(2,r.minus(2));if(!o.modPow(r.prev(),r).isUnit())return!1}return!0},u.prototype.isProbablePrime=o.prototype.isProbablePrime,o.prototype.next=function(){var e=this.value;return this.sign?b(e,1,this.sign):new o(m(e,1),this.sign)},u.prototype.next=function(){var e=this.value;return e+1<r?new u(e+1):new o(i,!1)},o.prototype.prev=function(){var e=this.value;return this.sign?new o(m(e,1),!0):b(e,1,this.sign)},u.prototype.prev=function(){var e=this.value;return e-1>-r?new u(e-1):new o(i,!0)};var _=[1];while(_[_.length-1]<=t)_.push(2*_[_.length-1]);var D=_.length,P=_[D-1];o.prototype.shiftLeft=function(e){if(!H(e))return e.isNegative()?this.shiftRight(e.abs()):this.times(J[2].pow(e));e=+e;if(e<0)return this.shiftRight(-e);var t=this;while(e>=D)t=t.multiply(P),e-=D-1;return t.multiply(_[e])},u.prototype.shiftLeft=o.prototype.shiftLeft,o.prototype.shiftRight=function(e){var t;if(!H(e))return e.isNegative()?this.shiftLeft(e.abs()):(t=this.divmod(J[2].pow(e)),t.remainder.isNegative()?t.quotient.prev():t.quotient);e=+e;if(e<0)return this.shiftLeft(-e);var n=this;while(e>=D){if(n.isZero())return n;t=A(n,P),n=t[1].isNegative()?t[0].prev():t[0],e-=D-1}return t=A(n,_[e]),t[1].isNegative()?t[0].prev():t[0]},u.prototype.shiftRight=o.prototype.shiftRight,o.prototype.not=function(){return this.negate().prev()},u.prototype.not=o.prototype.not,o.prototype.and=function(e){return B(this,e,function(e,t){return e&t})},u.prototype.and=o.prototype.and,o.prototype.or=function(e){return B(this,e,function(e,t){return e|t})},u.prototype.or=o.prototype.or,o.prototype.xor=function(e){return B(this,e,function(e,t){return e^t})},u.prototype.xor=o.prototype.xor;var U=function(e,t){var n=J[0],r=J[1],i=e.length;if(2<=t&&t<=36&&i<=s/Math.log(t))return new u(parseInt(e,t));t=$(t);var o=[],a,f=e[0]==="-";for(a=f?1:0;a<e.length;a++){var l=e[a].toLowerCase(),c=l.charCodeAt(0);if(48<=c&&c<=57)o.push($(l));else if(97<=c&&c<=122)o.push($(l.charCodeAt(0)-87));else{if(l!=="<")throw new Error(l+" is not a valid character");var h=a;do a++;while(e[a]!==">");o.push($(e.slice(h+1,a)))}}o.reverse();for(a=0;a<o.length;a++)n=n.add(o[a].times(r)),r=r.times(t);return f?n.negate():n};o.prototype.toString=function(t){t===e&&(t=10);if(t!==10)return W(this,t);var n=this.value,r=n.length,i=String(n[--r]),s="0000000",o;while(--r>=0)o=String(n[r]),i+=s.slice(o.length)+o;var u=this.sign?"-":"";return u+i},u.prototype.toString=function(t){return t===e&&(t=10),t!=10?W(this,t):String(this.value)},o.prototype.valueOf=function(){return+this.toString()},o.prototype.toJSNumber=o.prototype.valueOf,u.prototype.valueOf=function(){return this.value},u.prototype.toJSNumber=u.prototype.valueOf;var J=function(e,t){return typeof e=="undefined"?J[0]:typeof t!="undefined"?+t===10?$(e):U(e,t):$(e)};for(var K=0;K<1e3;K++)J[K]=new u(K),K>0&&(J[-K]=new u(-K));return J.one=J[1],J.zero=J[0],J.minusOne=J[-1],J.max=j,J.min=F,J.gcd=I,J.lcm=q,J.isInstance=function(e){return e instanceof o||e instanceof u},J.randBetween=R,J}();typeof module!="undefined"&&module.hasOwnProperty("exports")&&(module.exports=bigInt);