module.exports=function(e){var r={};function t(n){if(r[n])return r[n].exports;var i=r[n]={i:n,l:!1,exports:{}};return e[n].call(i.exports,i,i.exports,t),i.l=!0,i.exports}return t.m=e,t.c=r,t.d=function(e,r,n){t.o(e,r)||Object.defineProperty(e,r,{enumerable:!0,get:n})},t.r=function(e){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(e,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(e,"__esModule",{value:!0})},t.t=function(e,r){if(1&r&&(e=t(e)),8&r)return e;if(4&r&&"object"==typeof e&&e&&e.__esModule)return e;var n=Object.create(null);if(t.r(n),Object.defineProperty(n,"default",{enumerable:!0,value:e}),2&r&&"string"!=typeof e)for(var i in e)t.d(n,i,function(r){return e[r]}.bind(null,i));return n},t.n=function(e){var r=e&&e.__esModule?function(){return e.default}:function(){return e};return t.d(r,"a",r),r},t.o=function(e,r){return Object.prototype.hasOwnProperty.call(e,r)},t.p="",t(t.s=1)}([function(e,r,t){var n;!function(i){"use strict";var s,o=/^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,u=Math.ceil,f=Math.floor,l="[BigNumber Error] ",c=l+"Number primitive has more than 15 significant digits: ",a=1e14,h=14,p=9007199254740991,g=[1,10,100,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10,1e11,1e12,1e13],v=1e7,d=1e9;function w(e){var r=0|e;return e>0||e===r?r:r-1}function m(e){for(var r,t,n=1,i=e.length,s=e[0]+"";n<i;){for(r=e[n++]+"",t=h-r.length;t--;r="0"+r);s+=r}for(i=s.length;48===s.charCodeAt(--i););return s.slice(0,i+1||1)}function b(e,r){var t,n,i=e.c,s=r.c,o=e.s,u=r.s,f=e.e,l=r.e;if(!o||!u)return null;if(t=i&&!i[0],n=s&&!s[0],t||n)return t?n?0:-u:o;if(o!=u)return o;if(t=o<0,n=f==l,!i||!s)return n?0:!i^t?1:-1;if(!n)return f>l^t?1:-1;for(u=(f=i.length)<(l=s.length)?f:l,o=0;o<u;o++)if(i[o]!=s[o])return i[o]>s[o]^t?1:-1;return f==l?0:f>l^t?1:-1}function y(e,r,t,n){if(e<r||e>t||e!==f(e))throw Error(l+(n||"Argument")+("number"==typeof e?e<r||e>t?" out of range: ":" not an integer: ":" not a primitive number: ")+String(e))}function O(e){var r=e.c.length-1;return w(e.e/h)==r&&e.c[r]%2!=0}function N(e,r){return(e.length>1?e.charAt(0)+"."+e.slice(1):e)+(r<0?"e":"e+")+r}function E(e,r,t){var n,i;if(r<0){for(i=t+".";++r;i+=t);e=i+e}else if(++r>(n=e.length)){for(i=t,r-=n;--r;i+=t);e+=i}else r<n&&(e=e.slice(0,r)+"."+e.slice(r));return e}(s=function e(r){var t,n,i,s,x,A,S,_,P,T=G.prototype={constructor:G,toString:null,valueOf:null},I=new G(1),L=20,R=4,D=-7,M=21,B=-1e7,U=1e7,k=!1,C=1,z=0,j={prefix:"",groupSize:3,secondaryGroupSize:0,groupSeparator:",",decimalSeparator:".",fractionGroupSize:0,fractionGroupSeparator:" ",suffix:""},q="0123456789abcdefghijklmnopqrstuvwxyz";function G(e,r){var t,s,u,l,a,g,v,d,w=this;if(!(w instanceof G))return new G(e,r);if(null==r){if(e&&!0===e._isBigNumber)return w.s=e.s,void(!e.c||e.e>U?w.c=w.e=null:e.e<B?w.c=[w.e=0]:(w.e=e.e,w.c=e.c.slice()));if((g="number"==typeof e)&&0*e==0){if(w.s=1/e<0?(e=-e,-1):1,e===~~e){for(l=0,a=e;a>=10;a/=10,l++);return void(l>U?w.c=w.e=null:(w.e=l,w.c=[e]))}d=String(e)}else{if(!o.test(d=String(e)))return i(w,d,g);w.s=45==d.charCodeAt(0)?(d=d.slice(1),-1):1}(l=d.indexOf("."))>-1&&(d=d.replace(".","")),(a=d.search(/e/i))>0?(l<0&&(l=a),l+=+d.slice(a+1),d=d.substring(0,a)):l<0&&(l=d.length)}else{if(y(r,2,q.length,"Base"),10==r)return V(w=new G(e),L+w.e+1,R);if(d=String(e),g="number"==typeof e){if(0*e!=0)return i(w,d,g,r);if(w.s=1/e<0?(d=d.slice(1),-1):1,G.DEBUG&&d.replace(/^0\.0*|\./,"").length>15)throw Error(c+e)}else w.s=45===d.charCodeAt(0)?(d=d.slice(1),-1):1;for(t=q.slice(0,r),l=a=0,v=d.length;a<v;a++)if(t.indexOf(s=d.charAt(a))<0){if("."==s){if(a>l){l=v;continue}}else if(!u&&(d==d.toUpperCase()&&(d=d.toLowerCase())||d==d.toLowerCase()&&(d=d.toUpperCase()))){u=!0,a=-1,l=0;continue}return i(w,String(e),g,r)}g=!1,(l=(d=n(d,r,10,w.s)).indexOf("."))>-1?d=d.replace(".",""):l=d.length}for(a=0;48===d.charCodeAt(a);a++);for(v=d.length;48===d.charCodeAt(--v););if(d=d.slice(a,++v)){if(v-=a,g&&G.DEBUG&&v>15&&(e>p||e!==f(e)))throw Error(c+w.s*e);if((l=l-a-1)>U)w.c=w.e=null;else if(l<B)w.c=[w.e=0];else{if(w.e=l,w.c=[],a=(l+1)%h,l<0&&(a+=h),a<v){for(a&&w.c.push(+d.slice(0,a)),v-=h;a<v;)w.c.push(+d.slice(a,a+=h));a=h-(d=d.slice(a)).length}else a-=v;for(;a--;d+="0");w.c.push(+d)}}else w.c=[w.e=0]}function F(e,r,t,n){var i,s,o,u,f;if(null==t?t=R:y(t,0,8),!e.c)return e.toString();if(i=e.c[0],o=e.e,null==r)f=m(e.c),f=1==n||2==n&&(o<=D||o>=M)?N(f,o):E(f,o,"0");else if(s=(e=V(new G(e),r,t)).e,u=(f=m(e.c)).length,1==n||2==n&&(r<=s||s<=D)){for(;u<r;f+="0",u++);f=N(f,s)}else if(r-=o,f=E(f,s,"0"),s+1>u){if(--r>0)for(f+=".";r--;f+="0");}else if((r+=s-u)>0)for(s+1==u&&(f+=".");r--;f+="0");return e.s<0&&i?"-"+f:f}function H(e,r){for(var t,n=1,i=new G(e[0]);n<e.length;n++){if(!(t=new G(e[n])).s){i=t;break}r.call(i,t)&&(i=t)}return i}function $(e,r,t){for(var n=1,i=r.length;!r[--i];r.pop());for(i=r[0];i>=10;i/=10,n++);return(t=n+t*h-1)>U?e.c=e.e=null:t<B?e.c=[e.e=0]:(e.e=t,e.c=r),e}function V(e,r,t,n){var i,s,o,l,c,p,v,d=e.c,w=g;if(d){e:{for(i=1,l=d[0];l>=10;l/=10,i++);if((s=r-i)<0)s+=h,o=r,v=(c=d[p=0])/w[i-o-1]%10|0;else if((p=u((s+1)/h))>=d.length){if(!n)break e;for(;d.length<=p;d.push(0));c=v=0,i=1,o=(s%=h)-h+1}else{for(c=l=d[p],i=1;l>=10;l/=10,i++);v=(o=(s%=h)-h+i)<0?0:c/w[i-o-1]%10|0}if(n=n||r<0||null!=d[p+1]||(o<0?c:c%w[i-o-1]),n=t<4?(v||n)&&(0==t||t==(e.s<0?3:2)):v>5||5==v&&(4==t||n||6==t&&(s>0?o>0?c/w[i-o]:0:d[p-1])%10&1||t==(e.s<0?8:7)),r<1||!d[0])return d.length=0,n?(r-=e.e+1,d[0]=w[(h-r%h)%h],e.e=-r||0):d[0]=e.e=0,e;if(0==s?(d.length=p,l=1,p--):(d.length=p+1,l=w[h-s],d[p]=o>0?f(c/w[i-o]%w[o])*l:0),n)for(;;){if(0==p){for(s=1,o=d[0];o>=10;o/=10,s++);for(o=d[0]+=l,l=1;o>=10;o/=10,l++);s!=l&&(e.e++,d[0]==a&&(d[0]=1));break}if(d[p]+=l,d[p]!=a)break;d[p--]=0,l=1}for(s=d.length;0===d[--s];d.pop());}e.e>U?e.c=e.e=null:e.e<B&&(e.c=[e.e=0])}return e}function W(e){var r,t=e.e;return null===t?e.toString():(r=m(e.c),r=t<=D||t>=M?N(r,t):E(r,t,"0"),e.s<0?"-"+r:r)}return G.clone=e,G.ROUND_UP=0,G.ROUND_DOWN=1,G.ROUND_CEIL=2,G.ROUND_FLOOR=3,G.ROUND_HALF_UP=4,G.ROUND_HALF_DOWN=5,G.ROUND_HALF_EVEN=6,G.ROUND_HALF_CEIL=7,G.ROUND_HALF_FLOOR=8,G.EUCLID=9,G.config=G.set=function(e){var r,t;if(null!=e){if("object"!=typeof e)throw Error(l+"Object expected: "+e);if(e.hasOwnProperty(r="DECIMAL_PLACES")&&(y(t=e[r],0,d,r),L=t),e.hasOwnProperty(r="ROUNDING_MODE")&&(y(t=e[r],0,8,r),R=t),e.hasOwnProperty(r="EXPONENTIAL_AT")&&((t=e[r])&&t.pop?(y(t[0],-d,0,r),y(t[1],0,d,r),D=t[0],M=t[1]):(y(t,-d,d,r),D=-(M=t<0?-t:t))),e.hasOwnProperty(r="RANGE"))if((t=e[r])&&t.pop)y(t[0],-d,-1,r),y(t[1],1,d,r),B=t[0],U=t[1];else{if(y(t,-d,d,r),!t)throw Error(l+r+" cannot be zero: "+t);B=-(U=t<0?-t:t)}if(e.hasOwnProperty(r="CRYPTO")){if((t=e[r])!==!!t)throw Error(l+r+" not true or false: "+t);if(t){if("undefined"==typeof crypto||!crypto||!crypto.getRandomValues&&!crypto.randomBytes)throw k=!t,Error(l+"crypto unavailable");k=t}else k=t}if(e.hasOwnProperty(r="MODULO_MODE")&&(y(t=e[r],0,9,r),C=t),e.hasOwnProperty(r="POW_PRECISION")&&(y(t=e[r],0,d,r),z=t),e.hasOwnProperty(r="FORMAT")){if("object"!=typeof(t=e[r]))throw Error(l+r+" not an object: "+t);j=t}if(e.hasOwnProperty(r="ALPHABET")){if("string"!=typeof(t=e[r])||/^.$|[+-.\s]|(.).*\1/.test(t))throw Error(l+r+" invalid: "+t);q=t}}return{DECIMAL_PLACES:L,ROUNDING_MODE:R,EXPONENTIAL_AT:[D,M],RANGE:[B,U],CRYPTO:k,MODULO_MODE:C,POW_PRECISION:z,FORMAT:j,ALPHABET:q}},G.isBigNumber=function(e){if(!e||!0!==e._isBigNumber)return!1;if(!G.DEBUG)return!0;var r,t,n=e.c,i=e.e,s=e.s;e:if("[object Array]"=={}.toString.call(n)){if((1===s||-1===s)&&i>=-d&&i<=d&&i===f(i)){if(0===n[0]){if(0===i&&1===n.length)return!0;break e}if((r=(i+1)%h)<1&&(r+=h),String(n[0]).length==r){for(r=0;r<n.length;r++)if((t=n[r])<0||t>=a||t!==f(t))break e;if(0!==t)return!0}}}else if(null===n&&null===i&&(null===s||1===s||-1===s))return!0;throw Error(l+"Invalid BigNumber: "+e)},G.maximum=G.max=function(){return H(arguments,T.lt)},G.minimum=G.min=function(){return H(arguments,T.gt)},G.random=(s=9007199254740992*Math.random()&2097151?function(){return f(9007199254740992*Math.random())}:function(){return 8388608*(1073741824*Math.random()|0)+(8388608*Math.random()|0)},function(e){var r,t,n,i,o,c=0,a=[],p=new G(I);if(null==e?e=L:y(e,0,d),i=u(e/h),k)if(crypto.getRandomValues){for(r=crypto.getRandomValues(new Uint32Array(i*=2));c<i;)(o=131072*r[c]+(r[c+1]>>>11))>=9e15?(t=crypto.getRandomValues(new Uint32Array(2)),r[c]=t[0],r[c+1]=t[1]):(a.push(o%1e14),c+=2);c=i/2}else{if(!crypto.randomBytes)throw k=!1,Error(l+"crypto unavailable");for(r=crypto.randomBytes(i*=7);c<i;)(o=281474976710656*(31&r[c])+1099511627776*r[c+1]+4294967296*r[c+2]+16777216*r[c+3]+(r[c+4]<<16)+(r[c+5]<<8)+r[c+6])>=9e15?crypto.randomBytes(7).copy(r,c):(a.push(o%1e14),c+=7);c=i/7}if(!k)for(;c<i;)(o=s())<9e15&&(a[c++]=o%1e14);for(i=a[--c],e%=h,i&&e&&(o=g[h-e],a[c]=f(i/o)*o);0===a[c];a.pop(),c--);if(c<0)a=[n=0];else{for(n=-1;0===a[0];a.splice(0,1),n-=h);for(c=1,o=a[0];o>=10;o/=10,c++);c<h&&(n-=h-c)}return p.e=n,p.c=a,p}),G.sum=function(){for(var e=1,r=arguments,t=new G(r[0]);e<r.length;)t=t.plus(r[e++]);return t},n=function(){function e(e,r,t,n){for(var i,s,o=[0],u=0,f=e.length;u<f;){for(s=o.length;s--;o[s]*=r);for(o[0]+=n.indexOf(e.charAt(u++)),i=0;i<o.length;i++)o[i]>t-1&&(null==o[i+1]&&(o[i+1]=0),o[i+1]+=o[i]/t|0,o[i]%=t)}return o.reverse()}return function(r,n,i,s,o){var u,f,l,c,a,h,p,g,v=r.indexOf("."),d=L,w=R;for(v>=0&&(c=z,z=0,r=r.replace(".",""),h=(g=new G(n)).pow(r.length-v),z=c,g.c=e(E(m(h.c),h.e,"0"),10,i,"0123456789"),g.e=g.c.length),l=c=(p=e(r,n,i,o?(u=q,"0123456789"):(u="0123456789",q))).length;0==p[--c];p.pop());if(!p[0])return u.charAt(0);if(v<0?--l:(h.c=p,h.e=l,h.s=s,p=(h=t(h,g,d,w,i)).c,a=h.r,l=h.e),v=p[f=l+d+1],c=i/2,a=a||f<0||null!=p[f+1],a=w<4?(null!=v||a)&&(0==w||w==(h.s<0?3:2)):v>c||v==c&&(4==w||a||6==w&&1&p[f-1]||w==(h.s<0?8:7)),f<1||!p[0])r=a?E(u.charAt(1),-d,u.charAt(0)):u.charAt(0);else{if(p.length=f,a)for(--i;++p[--f]>i;)p[f]=0,f||(++l,p=[1].concat(p));for(c=p.length;!p[--c];);for(v=0,r="";v<=c;r+=u.charAt(p[v++]));r=E(r,l,u.charAt(0))}return r}}(),t=function(){function e(e,r,t){var n,i,s,o,u=0,f=e.length,l=r%v,c=r/v|0;for(e=e.slice();f--;)u=((i=l*(s=e[f]%v)+(n=c*s+(o=e[f]/v|0)*l)%v*v+u)/t|0)+(n/v|0)+c*o,e[f]=i%t;return u&&(e=[u].concat(e)),e}function r(e,r,t,n){var i,s;if(t!=n)s=t>n?1:-1;else for(i=s=0;i<t;i++)if(e[i]!=r[i]){s=e[i]>r[i]?1:-1;break}return s}function t(e,r,t,n){for(var i=0;t--;)e[t]-=i,i=e[t]<r[t]?1:0,e[t]=i*n+e[t]-r[t];for(;!e[0]&&e.length>1;e.splice(0,1));}return function(n,i,s,o,u){var l,c,p,g,v,d,m,b,y,O,N,E,x,A,S,_,P,T=n.s==i.s?1:-1,I=n.c,L=i.c;if(!(I&&I[0]&&L&&L[0]))return new G(n.s&&i.s&&(I?!L||I[0]!=L[0]:L)?I&&0==I[0]||!L?0*T:T/0:NaN);for(y=(b=new G(T)).c=[],T=s+(c=n.e-i.e)+1,u||(u=a,c=w(n.e/h)-w(i.e/h),T=T/h|0),p=0;L[p]==(I[p]||0);p++);if(L[p]>(I[p]||0)&&c--,T<0)y.push(1),g=!0;else{for(A=I.length,_=L.length,p=0,T+=2,(v=f(u/(L[0]+1)))>1&&(L=e(L,v,u),I=e(I,v,u),_=L.length,A=I.length),x=_,N=(O=I.slice(0,_)).length;N<_;O[N++]=0);P=L.slice(),P=[0].concat(P),S=L[0],L[1]>=u/2&&S++;do{if(v=0,(l=r(L,O,_,N))<0){if(E=O[0],_!=N&&(E=E*u+(O[1]||0)),(v=f(E/S))>1)for(v>=u&&(v=u-1),m=(d=e(L,v,u)).length,N=O.length;1==r(d,O,m,N);)v--,t(d,_<m?P:L,m,u),m=d.length,l=1;else 0==v&&(l=v=1),m=(d=L.slice()).length;if(m<N&&(d=[0].concat(d)),t(O,d,N,u),N=O.length,-1==l)for(;r(L,O,_,N)<1;)v++,t(O,_<N?P:L,N,u),N=O.length}else 0===l&&(v++,O=[0]);y[p++]=v,O[0]?O[N++]=I[x]||0:(O=[I[x]],N=1)}while((x++<A||null!=O[0])&&T--);g=null!=O[0],y[0]||y.splice(0,1)}if(u==a){for(p=1,T=y[0];T>=10;T/=10,p++);V(b,s+(b.e=p+c*h-1)+1,o,g)}else b.e=c,b.r=+g;return b}}(),x=/^(-?)0([xbo])(?=\w[\w.]*$)/i,A=/^([^.]+)\.$/,S=/^\.([^.]+)$/,_=/^-?(Infinity|NaN)$/,P=/^\s*\+(?=[\w.])|^\s+|\s+$/g,i=function(e,r,t,n){var i,s=t?r:r.replace(P,"");if(_.test(s))e.s=isNaN(s)?null:s<0?-1:1;else{if(!t&&(s=s.replace(x,function(e,r,t){return i="x"==(t=t.toLowerCase())?16:"b"==t?2:8,n&&n!=i?e:r}),n&&(i=n,s=s.replace(A,"$1").replace(S,"0.$1")),r!=s))return new G(s,i);if(G.DEBUG)throw Error(l+"Not a"+(n?" base "+n:"")+" number: "+r);e.s=null}e.c=e.e=null},T.absoluteValue=T.abs=function(){var e=new G(this);return e.s<0&&(e.s=1),e},T.comparedTo=function(e,r){return b(this,new G(e,r))},T.decimalPlaces=T.dp=function(e,r){var t,n,i,s=this;if(null!=e)return y(e,0,d),null==r?r=R:y(r,0,8),V(new G(s),e+s.e+1,r);if(!(t=s.c))return null;if(n=((i=t.length-1)-w(this.e/h))*h,i=t[i])for(;i%10==0;i/=10,n--);return n<0&&(n=0),n},T.dividedBy=T.div=function(e,r){return t(this,new G(e,r),L,R)},T.dividedToIntegerBy=T.idiv=function(e,r){return t(this,new G(e,r),0,1)},T.exponentiatedBy=T.pow=function(e,r){var t,n,i,s,o,c,a,p,g=this;if((e=new G(e)).c&&!e.isInteger())throw Error(l+"Exponent not an integer: "+W(e));if(null!=r&&(r=new G(r)),o=e.e>14,!g.c||!g.c[0]||1==g.c[0]&&!g.e&&1==g.c.length||!e.c||!e.c[0])return p=new G(Math.pow(+W(g),o?2-O(e):+W(e))),r?p.mod(r):p;if(c=e.s<0,r){if(r.c?!r.c[0]:!r.s)return new G(NaN);(n=!c&&g.isInteger()&&r.isInteger())&&(g=g.mod(r))}else{if(e.e>9&&(g.e>0||g.e<-1||(0==g.e?g.c[0]>1||o&&g.c[1]>=24e7:g.c[0]<8e13||o&&g.c[0]<=9999975e7)))return s=g.s<0&&O(e)?-0:0,g.e>-1&&(s=1/s),new G(c?1/s:s);z&&(s=u(z/h+2))}for(o?(t=new G(.5),c&&(e.s=1),a=O(e)):a=(i=Math.abs(+W(e)))%2,p=new G(I);;){if(a){if(!(p=p.times(g)).c)break;s?p.c.length>s&&(p.c.length=s):n&&(p=p.mod(r))}if(i){if(0===(i=f(i/2)))break;a=i%2}else if(V(e=e.times(t),e.e+1,1),e.e>14)a=O(e);else{if(0==(i=+W(e)))break;a=i%2}g=g.times(g),s?g.c&&g.c.length>s&&(g.c.length=s):n&&(g=g.mod(r))}return n?p:(c&&(p=I.div(p)),r?p.mod(r):s?V(p,z,R,void 0):p)},T.integerValue=function(e){var r=new G(this);return null==e?e=R:y(e,0,8),V(r,r.e+1,e)},T.isEqualTo=T.eq=function(e,r){return 0===b(this,new G(e,r))},T.isFinite=function(){return!!this.c},T.isGreaterThan=T.gt=function(e,r){return b(this,new G(e,r))>0},T.isGreaterThanOrEqualTo=T.gte=function(e,r){return 1===(r=b(this,new G(e,r)))||0===r},T.isInteger=function(){return!!this.c&&w(this.e/h)>this.c.length-2},T.isLessThan=T.lt=function(e,r){return b(this,new G(e,r))<0},T.isLessThanOrEqualTo=T.lte=function(e,r){return-1===(r=b(this,new G(e,r)))||0===r},T.isNaN=function(){return!this.s},T.isNegative=function(){return this.s<0},T.isPositive=function(){return this.s>0},T.isZero=function(){return!!this.c&&0==this.c[0]},T.minus=function(e,r){var t,n,i,s,o=this,u=o.s;if(r=(e=new G(e,r)).s,!u||!r)return new G(NaN);if(u!=r)return e.s=-r,o.plus(e);var f=o.e/h,l=e.e/h,c=o.c,p=e.c;if(!f||!l){if(!c||!p)return c?(e.s=-r,e):new G(p?o:NaN);if(!c[0]||!p[0])return p[0]?(e.s=-r,e):new G(c[0]?o:3==R?-0:0)}if(f=w(f),l=w(l),c=c.slice(),u=f-l){for((s=u<0)?(u=-u,i=c):(l=f,i=p),i.reverse(),r=u;r--;i.push(0));i.reverse()}else for(n=(s=(u=c.length)<(r=p.length))?u:r,u=r=0;r<n;r++)if(c[r]!=p[r]){s=c[r]<p[r];break}if(s&&(i=c,c=p,p=i,e.s=-e.s),(r=(n=p.length)-(t=c.length))>0)for(;r--;c[t++]=0);for(r=a-1;n>u;){if(c[--n]<p[n]){for(t=n;t&&!c[--t];c[t]=r);--c[t],c[n]+=a}c[n]-=p[n]}for(;0==c[0];c.splice(0,1),--l);return c[0]?$(e,c,l):(e.s=3==R?-1:1,e.c=[e.e=0],e)},T.modulo=T.mod=function(e,r){var n,i,s=this;return e=new G(e,r),!s.c||!e.s||e.c&&!e.c[0]?new G(NaN):!e.c||s.c&&!s.c[0]?new G(s):(9==C?(i=e.s,e.s=1,n=t(s,e,0,3),e.s=i,n.s*=i):n=t(s,e,0,C),(e=s.minus(n.times(e))).c[0]||1!=C||(e.s=s.s),e)},T.multipliedBy=T.times=function(e,r){var t,n,i,s,o,u,f,l,c,p,g,d,m,b,y,O=this,N=O.c,E=(e=new G(e,r)).c;if(!(N&&E&&N[0]&&E[0]))return!O.s||!e.s||N&&!N[0]&&!E||E&&!E[0]&&!N?e.c=e.e=e.s=null:(e.s*=O.s,N&&E?(e.c=[0],e.e=0):e.c=e.e=null),e;for(n=w(O.e/h)+w(e.e/h),e.s*=O.s,(f=N.length)<(p=E.length)&&(m=N,N=E,E=m,i=f,f=p,p=i),i=f+p,m=[];i--;m.push(0));for(b=a,y=v,i=p;--i>=0;){for(t=0,g=E[i]%y,d=E[i]/y|0,s=i+(o=f);s>i;)t=((l=g*(l=N[--o]%y)+(u=d*l+(c=N[o]/y|0)*g)%y*y+m[s]+t)/b|0)+(u/y|0)+d*c,m[s--]=l%b;m[s]=t}return t?++n:m.splice(0,1),$(e,m,n)},T.negated=function(){var e=new G(this);return e.s=-e.s||null,e},T.plus=function(e,r){var t,n=this,i=n.s;if(r=(e=new G(e,r)).s,!i||!r)return new G(NaN);if(i!=r)return e.s=-r,n.minus(e);var s=n.e/h,o=e.e/h,u=n.c,f=e.c;if(!s||!o){if(!u||!f)return new G(i/0);if(!u[0]||!f[0])return f[0]?e:new G(u[0]?n:0*i)}if(s=w(s),o=w(o),u=u.slice(),i=s-o){for(i>0?(o=s,t=f):(i=-i,t=u),t.reverse();i--;t.push(0));t.reverse()}for((i=u.length)-(r=f.length)<0&&(t=f,f=u,u=t,r=i),i=0;r;)i=(u[--r]=u[r]+f[r]+i)/a|0,u[r]=a===u[r]?0:u[r]%a;return i&&(u=[i].concat(u),++o),$(e,u,o)},T.precision=T.sd=function(e,r){var t,n,i,s=this;if(null!=e&&e!==!!e)return y(e,1,d),null==r?r=R:y(r,0,8),V(new G(s),e,r);if(!(t=s.c))return null;if(n=(i=t.length-1)*h+1,i=t[i]){for(;i%10==0;i/=10,n--);for(i=t[0];i>=10;i/=10,n++);}return e&&s.e+1>n&&(n=s.e+1),n},T.shiftedBy=function(e){return y(e,-p,p),this.times("1e"+e)},T.squareRoot=T.sqrt=function(){var e,r,n,i,s,o=this,u=o.c,f=o.s,l=o.e,c=L+4,a=new G("0.5");if(1!==f||!u||!u[0])return new G(!f||f<0&&(!u||u[0])?NaN:u?o:1/0);if(0==(f=Math.sqrt(+W(o)))||f==1/0?(((r=m(u)).length+l)%2==0&&(r+="0"),f=Math.sqrt(+r),l=w((l+1)/2)-(l<0||l%2),n=new G(r=f==1/0?"1e"+l:(r=f.toExponential()).slice(0,r.indexOf("e")+1)+l)):n=new G(f+""),n.c[0])for((f=(l=n.e)+c)<3&&(f=0);;)if(s=n,n=a.times(s.plus(t(o,s,c,1))),m(s.c).slice(0,f)===(r=m(n.c)).slice(0,f)){if(n.e<l&&--f,"9999"!=(r=r.slice(f-3,f+1))&&(i||"4999"!=r)){+r&&(+r.slice(1)||"5"!=r.charAt(0))||(V(n,n.e+L+2,1),e=!n.times(n).eq(o));break}if(!i&&(V(s,s.e+L+2,0),s.times(s).eq(o))){n=s;break}c+=4,f+=4,i=1}return V(n,n.e+L+1,R,e)},T.toExponential=function(e,r){return null!=e&&(y(e,0,d),e++),F(this,e,r,1)},T.toFixed=function(e,r){return null!=e&&(y(e,0,d),e=e+this.e+1),F(this,e,r)},T.toFormat=function(e,r,t){var n,i=this;if(null==t)null!=e&&r&&"object"==typeof r?(t=r,r=null):e&&"object"==typeof e?(t=e,e=r=null):t=j;else if("object"!=typeof t)throw Error(l+"Argument not an object: "+t);if(n=i.toFixed(e,r),i.c){var s,o=n.split("."),u=+t.groupSize,f=+t.secondaryGroupSize,c=t.groupSeparator||"",a=o[0],h=o[1],p=i.s<0,g=p?a.slice(1):a,v=g.length;if(f&&(s=u,u=f,f=s,v-=s),u>0&&v>0){for(s=v%u||u,a=g.substr(0,s);s<v;s+=u)a+=c+g.substr(s,u);f>0&&(a+=c+g.slice(s)),p&&(a="-"+a)}n=h?a+(t.decimalSeparator||"")+((f=+t.fractionGroupSize)?h.replace(new RegExp("\\d{"+f+"}\\B","g"),"$&"+(t.fractionGroupSeparator||"")):h):a}return(t.prefix||"")+n+(t.suffix||"")},T.toFraction=function(e){var r,n,i,s,o,u,f,c,a,p,v,d,w=this,b=w.c;if(null!=e&&(!(f=new G(e)).isInteger()&&(f.c||1!==f.s)||f.lt(I)))throw Error(l+"Argument "+(f.isInteger()?"out of range: ":"not an integer: ")+W(f));if(!b)return new G(w);for(r=new G(I),a=n=new G(I),i=c=new G(I),d=m(b),o=r.e=d.length-w.e-1,r.c[0]=g[(u=o%h)<0?h+u:u],e=!e||f.comparedTo(r)>0?o>0?r:a:f,u=U,U=1/0,f=new G(d),c.c[0]=0;p=t(f,r,0,1),1!=(s=n.plus(p.times(i))).comparedTo(e);)n=i,i=s,a=c.plus(p.times(s=a)),c=s,r=f.minus(p.times(s=r)),f=s;return s=t(e.minus(n),i,0,1),c=c.plus(s.times(a)),n=n.plus(s.times(i)),c.s=a.s=w.s,v=t(a,i,o*=2,R).minus(w).abs().comparedTo(t(c,n,o,R).minus(w).abs())<1?[a,i]:[c,n],U=u,v},T.toNumber=function(){return+W(this)},T.toPrecision=function(e,r){return null!=e&&y(e,1,d),F(this,e,r,2)},T.toString=function(e){var r,t=this,i=t.s,s=t.e;return null===s?i?(r="Infinity",i<0&&(r="-"+r)):r="NaN":(null==e?r=s<=D||s>=M?N(m(t.c),s):E(m(t.c),s,"0"):10===e?r=E(m((t=V(new G(t),L+s+1,R)).c),t.e,"0"):(y(e,2,q.length,"Base"),r=n(E(m(t.c),s,"0"),10,e,i,!0)),i<0&&t.c[0]&&(r="-"+r)),r},T.valueOf=T.toJSON=function(){return W(this)},T._isBigNumber=!0,null!=r&&G.set(r),G}()).default=s.BigNumber=s,void 0===(n=function(){return s}.call(r,t,r,e))||(e.exports=n)}()},function(e,r,t){"use strict";var n=t(2);t(3)(n.readFileSync("/dev/stdin","utf8"))},function(e,r){e.exports=require("fs")},function(e,r,t){"use strict";var n=t(4),i=t(6);e.exports=function(e){var r=new n(e);i(r)}},function(e,r,t){"use strict";var n=t(5),i=t(0);e.exports=class{constructor(e){var r=e.trim().split(/\s+/g);this.inp=new n(r)}inr(){return this.inp.deq()}in(){return new i(this.inp.deq())}fin(){this.inp.clear()}}},function(e,r,t){"use strict";e.exports=class{constructor(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:[];this.size=e.length,this.items=e,this.ind=0}enq(e){this.size+=1,this.items.push(e)}deq(){var e=this.items[this.ind];return this.size-=1,this.ind+=1,e}clear(){this.items=[],this.size=0,this.ind=0}}},function(e,r,t){"use strict";var n=t(0),i=t(7);e.exports=function(e){for(var r=e.in(),t=e.in(),s=new i([],!0,function(e,r){return r.comparedTo(e)>0}),o=0;o<r;o++){var u=e.in();s.pushItem(u)}for(var f=0;f<t;f++){var l=s.getTop();s.removeTop(),s.pushItem(l.idiv(2))}for(var c=new n(0),a=s.getValuesList(),h=0;h<r;h++)c=c.plus(a[h]);console.log(c.toString())}},function(e,r,t){"use strict";function n(e,r){return e<=r}function i(e,r){return e>=r}function s(e){return e.toString()}e.exports=class{constructor(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:[],r=!(arguments.length>1&&void 0!==arguments[1])||arguments[1],t=arguments.length>2&&void 0!==arguments[2]?arguments[2]:void 0,o=arguments.length>3&&void 0!==arguments[3]?arguments[3]:s;this.cf=r?n:i,this.kgf=o,this.table=new Map;var u=e.length;this.heap=new Array(u);for(var f=0;f<u;f++){var l={value:e[f],index:f};this.heap[f]=l;var c=this.kgf(e[f]);this.table[c]=l}t&&(this.cf=t),this.size=this.heap.length,this.heapify()}findItem(e){var r=this.kgf(e);return this.table[r]}heapify(){for(var e=0,r=this.size;2*e+1<=r;)e=2*e+1;for(var t=e-1;t>=0;)2*t+1>r-1?t--:(this.downHeap(t),t--)}downHeap(e){for(var r=this.size,t=e;2*t+1<=r-1;){var n=this.heap[2*t+1],i=2*t+2<=r-1?this.heap[2*t+2]:n,s=this.cf(i.value,n.value)?n:i,o=this.cf(i.value,n.value)?2*t+1:2*t+2;if(this.cf(s.value,this.heap[t].value))break;var u=s;this.heap[o]=this.heap[t],this.heap[t]=u,this.heap[o].index=o,this.heap[t].index=t,t=o}}upHeap(e){for(var r=e;0!=r;){var t=Math.floor((r-1)/2);if(this.cf(this.heap[r].value,this.heap[t].value))break;var n=this.heap[t];this.heap[t]=this.heap[r],this.heap[r]=n,this.heap[r].index=r,this.heap[t].index=t,r=t}}pushItem(e){this.size+=1;var r=this.heap.length,t={value:e,index:r};this.heap.push(t);var n=this.kgf(e);this.table[n]=t,this.upHeap(r)}getTop(){return this.heap[0].value}removeTop(){if(0==this.size)return!1;this.size-=1;var e=this.heap[0],r=this.kgf(e.value);return this.table[r]=void 0,this.heap[0]=this.heap.pop(),this.heap[0].index=0,this.downHeap(0),!0}getValuesList(){for(var e=this.heap.length,r=[],t=0;t<e;t++)r.push(this.heap[t].value);return r}}}]);