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&&A(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 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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){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 N(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=k(f,a)[0],[l(o),l(f)]}function C(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(A(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(A(p,o)<=0)break;a--}while(a);s.push(a),o=g(o,p)}return s.reverse(),[l(s),l(o)]}function k(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 L(e,n){var r,i=z(n),s=e.value,a=i.value,c;if(a===0)throw new Error("Cannot divide by 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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 H(e,t){return e=z(e),t=z(t),e.greater(t)?e:t}function B(e,t){return e=z(e),t=z(t),e.lesser(t)?e:t}function j(e,t){return e=z(e).abs(),t=z(t).abs(),e.equals(t)?e:e.isZero()?t:t.isZero()?e:e.isEven()?t.isOdd()?j(e.divide(2),t):j(e.divide(2),t.divide(2)).multiply(2):t.isEven()?j(e,t.divide(2)):e.greater(t)?j(e.subtract(t).divide(2),t):j(t.subtract(e).divide(2),e)}function F(e,t){return e=z(e).abs(),t=z(t).abs(),e.multiply(t).divide(j(e,t))}function I(e,n){e=z(e),n=z(n);var r=B(e,n),i=H(e,n),s=i.subtract(r);if(s.isSmall)return r.add(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 R(e){var t=e.value;return typeof t=="number"&&(t=[t]),t.length===1&&t[0]<=36?"0123456789abcdefghijklmnopqrstuvwxyz".charAt(t[0]):"<"+t+">"}function U(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(R(o))}return r.push(R(i)),n+r.reverse().join("")}function z(e){if(e instanceof o||e instanceof u)return e;if(typeof e=="number"){if(a(e))return new u(e);e=String(e)}if(typeof e=="string"){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)}}var t=1e7,n=7,r=9007199254740992,i=f(r),s=Math.log(r);o.prototype.add=function(e){var t,n=z(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=z(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=z(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=z(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=z(e),i=this.value,s=r.value,u=this.sign!==r.sign,a;if(r.isSmall){if(s===0)return W[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.multiply=function(e){var n=z(e),r=this.value,i=n.value;if(r===0)return W[0];if(r===1)return n;if(r===-1)return n.negate();if(n.isSmall){if(a(r*i))return new u(r*i);i=f(Math.abs(i))}var s=Math.abs(r);return s<t?new o(E(i,s),this.sign!==n.sign):new o(w(i,f(s)),this.sign!==n.sign)},u.prototype.times=u.prototype.multiply,o.prototype.square=function(){return new o(T(this.value),!1)},u.prototype.square=function(){var e=this.value*this.value;return a(e)?new u(e):new o(T(f(Math.abs(this.value))),!1)},o.prototype.divmod=function(e){var t=L(this,e);return{quotient:t[0],remainder:t[1]}},u.prototype.divmod=o.prototype.divmod,o.prototype.divide=function(e){return L(this,e)[0]},u.prototype.over=u.prototype.divide=o.prototype.over=o.prototype.divide,o.prototype.mod=function(e){return L(this,e)[1]},u.prototype.remainder=u.prototype.mod=o.prototype.remainder=o.prototype.mod,o.prototype.pow=function(e){var t=z(e),n=this.value,r=t.value,i,s,o;if(r===0)return W[1];if(n===0)return W[0];if(n===1)return W[1];if(n===-1)return t.isEven()?W[1]:W[-1];if(t.sign)return W[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=W[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=z(e),t=z(t);if(t.isZero())throw new Error("Cannot take modPow with modulus 0");var n=W[1],r=this.mod(t);if(r.isZero())return W[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=z(e),n=this.value,r=t.value;return t.isSmall?1:A(n,r)},u.prototype.compareAbs=function(e){var t=z(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=z(e),n=this.value,r=t.value;return this.sign!==t.sign?t.sign?1:-1:t.isSmall?this.sign?-1:1:A(n,r)*(this.sign?-1:1)},o.prototype.compareTo=o.prototype.compare,u.prototype.compare=function(e){var t=z(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=z(e),n=t.value;return n===0?!1:n===1?!0:n===2?this.isEven():this.mod(t).equals(W[0])},u.prototype.isDivisibleBy=o.prototype.isDivisibleBy,o.prototype.isPrime=function(){var e=this.abs(),t=e.prev();if(e.isUnit())return!1;if(e.equals(2)||e.equals(3)||e.equals(5))return!0;if(e.isEven()||e.isDivisibleBy(3)||e.isDivisibleBy(5))return!1;if(e.lesser(25))return!0;var n=[2,3,5,7,11,13,17,19],r=t,i,s,o,u;while(r.isEven())r=r.divide(2);for(o=0;o<n.length;o++){u=bigInt(n[o]).modPow(r,e);if(u.equals(W[1])||u.equals(t))continue;for(s=!0,i=r;s&&i.lesser(t);i=i.multiply(2))u=u.square().mod(e),u.equals(t)&&(s=!1);if(s)return!1}return!0},u.prototype.isPrime=o.prototype.isPrime,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 O=[1];while(O[O.length-1]<=t)O.push(2*O[O.length-1]);var M=O.length,_=O[M-1];o.prototype.shiftLeft=function(e){if(!D(e))return e.isNegative()?this.shiftRight(e.abs()):this.times(W[2].pow(e));e=+e;if(e<0)return this.shiftRight(-e);var t=this;while(e>=M)t=t.multiply(_),e-=M-1;return t.multiply(O[e])},u.prototype.shiftLeft=o.prototype.shiftLeft,o.prototype.shiftRight=function(e){var t;if(!D(e))return e.isNegative()?this.shiftLeft(e.abs()):(t=this.divmod(W[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>=M){if(n.isZero())return n;t=L(n,_),n=t[1].isNegative()?t[0].prev():t[0],e-=M-1}return t=L(n,O[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 P(this,e,function(e,t){return e&t})},u.prototype.and=o.prototype.and,o.prototype.or=function(e){return P(this,e,function(e,t){return e|t})},u.prototype.or=o.prototype.or,o.prototype.xor=function(e){return P(this,e,function(e,t){return e^t})},u.prototype.xor=o.prototype.xor;var q=function(e,t){var n=W[0],r=W[1],i=e.length;if(2<=t&&t<=36&&i<=s/Math.log(t))return new u(parseInt(e,t));t=z(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(z(l));else if(97<=c&&c<=122)o.push(z(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(z(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 U(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?U(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 W=function(e,t){return typeof e=="undefined"?W[0]:typeof t!="undefined"?+t===10?z(e):q(e,t):z(e)};for(var X=0;X<1e3;X++)W[X]=new u(X),X>0&&(W[-X]=new u(-X));return W.one=W[1],W.zero=W[0],W.minusOne=W[-1],W.max=H,W.min=B,W.gcd=j,W.lcm=F,W.isInstance=function(e){return e instanceof o||e instanceof u},W.randBetween=I,W}();typeof module!="undefined"&&module.hasOwnProperty("exports")&&(module.exports=bigInt);