var dbits;var canary=244837814094590;var j_lm=((canary&16777215)==15715070);function BigInteger(a,b,c){if(a!=null){if("number"==typeof a){this.fromNumber(a,b,c)}else{if(b==null&&"string"!=typeof a){this.fromString(a,256)}else{this.fromString(a,b)}}}}function nbi(){return new BigInteger(null)}function am1(i,x,w,j,c,n){while(--n>=0){var v=x*this[i++]+w[j]+c;c=Math.floor(v/67108864);w[j++]=v&67108863}return c}function am2(i,x,w,j,c,n){var xl=x&32767,xh=x>>15;while(--n>=0){var l=this[i]&32767;var h=this[i++]>>15;var m=xh*l+h*xl;l=xl*l+((m&32767)<<15)+w[j]+(c&1073741823);c=(l>>>30)+(m>>>15)+xh*h+(c>>>30);w[j++]=l&1073741823}return c}function am3(i,x,w,j,c,n){var xl=x&16383,xh=x>>14;while(--n>=0){var l=this[i]&16383;var h=this[i++]>>14;var m=xh*l+h*xl;l=xl*l+((m&16383)<<14)+w[j]+c;c=(l>>28)+(m>>14)+xh*h;w[j++]=l&268435455}return c}if(j_lm&&(navigator.appName=="Microsoft Internet Explorer")){BigInteger.prototype.am=am2;dbits=30}else{if(j_lm&&(navigator.appName!="Netscape")){BigInteger.prototype.am=am1;dbits=26}else{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 BI_RM="0123456789abcdefghijklmnopqrstuvwxyz";var BI_RC=new Array();var rr,vv;rr="0".charCodeAt(0);for(vv=0;vv<=9;++vv){BI_RC[rr++]=vv}rr="a".charCodeAt(0);for(vv=10;vv<36;++vv){BI_RC[rr++]=vv}rr="A".charCodeAt(0);for(vv=10;vv<36;++vv){BI_RC[rr++]=vv}function int2char(n){return BI_RM.charAt(n)}function intAt(s,i){var c=BI_RC[s.charCodeAt(i)];return(c==null)?-1:c}function bnpCopyTo(r){for(var i=this.t-1;i>=0;--i){r[i]=this[i]}r.t=this.t;r.s=this.s}function bnpFromInt(x){this.t=1;this.s=(x<0)?-1:0;if(x>0){this[0]=x}else{if(x<-1){this[0]=x+this.DV}else{this.t=0}}}function nbv(i){var r=nbi();r.fromInt(i);return r}function bnpFromString(s,b){var k;if(b==16){k=4}else{if(b==8){k=3}else{if(b==256){k=8}else{if(b==2){k=1}else{if(b==32){k=5}else{if(b==4){k=2}else{this.fromRadix(s,b);return}}}}}}this.t=0;this.s=0;var i=s.length,mi=false,sh=0;while(--i>=0){var x=(k==8)?s[i]&255:intAt(s,i);if(x<0){if(s.charAt(i)=="-"){mi=true}continue}mi=false;if(sh==0){this[this.t++]=x}else{if(sh+k>this.DB){this[this.t-1]|=(x&((1<<(this.DB-sh))-1))<<sh;this[this.t++]=(x>>(this.DB-sh))}else{this[this.t-1]|=x<<sh}}sh+=k;if(sh>=this.DB){sh-=this.DB}}if(k==8&&(s[0]&128)!=0){this.s=-1;if(sh>0){this[this.t-1]|=((1<<(this.DB-sh))-1)<<sh}}this.clamp();if(mi){BigInteger.ZERO.subTo(this,this)}}function bnpClamp(){var c=this.s&this.DM;while(this.t>0&&this[this.t-1]==c){--this.t}}function bnToString(b){if(this.s<0){return"-"+this.negate().toString(b)}var k;if(b==16){k=4}else{if(b==8){k=3}else{if(b==2){k=1}else{if(b==32){k=5}else{if(b==4){k=2}else{return this.toRadix(b)}}}}}var km=(1<<k)-1,d,m=false,r="",i=this.t;var p=this.DB-(i*this.DB)%k;if(i-->0){if(p<this.DB&&(d=this[i]>>p)>0){m=true;r=int2char(d)}while(i>=0){if(p<k){d=(this[i]&((1<<p)-1))<<(k-p);d|=this[--i]>>(p+=this.DB-k)}else{d=(this[i]>>(p-=k))&km;if(p<=0){p+=this.DB;--i}}if(d>0){m=true}if(m){r+=int2char(d)}}}return m?r:"0"}function bnNegate(){var r=nbi();BigInteger.ZERO.subTo(this,r);return r}function bnAbs(){return(this.s<0)?this.negate():this}function bnCompareTo(a){var r=this.s-a.s;if(r!=0){return r}var i=this.t;r=i-a.t;if(r!=0){return(this.s<0)?-r:r}while(--i>=0){if((r=this[i]-a[i])!=0){return r}}return 0}function nbits(x){var r=1,t;if((t=x>>>16)!=0){x=t;r+=16}if((t=x>>8)!=0){x=t;r+=8}if((t=x>>4)!=0){x=t;r+=4}if((t=x>>2)!=0){x=t;r+=2}if((t=x>>1)!=0){x=t;r+=1}return r}function bnBitLength(){if(this.t<=0){return 0}return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM))}function bnpDLShiftTo(n,r){var i;for(i=this.t-1;i>=0;--i){r[i+n]=this[i]}for(i=n-1;i>=0;--i){r[i]=0}r.t=this.t+n;r.s=this.s}function bnpDRShiftTo(n,r){for(var i=n;i<this.t;++i){r[i-n]=this[i]}r.t=Math.max(this.t-n,0);r.s=this.s}function bnpLShiftTo(n,r){var bs=n%this.DB;var cbs=this.DB-bs;var bm=(1<<cbs)-1;var ds=Math.floor(n/this.DB),c=(this.s<<bs)&this.DM,i;for(i=this.t-1;i>=0;--i){r[i+ds+1]=(this[i]>>cbs)|c;c=(this[i]&bm)<<bs}for(i=ds-1;i>=0;--i){r[i]=0}r[ds]=c;r.t=this.t+ds+1;r.s=this.s;r.clamp()}function bnpRShiftTo(n,r){r.s=this.s;var ds=Math.floor(n/this.DB);if(ds>=this.t){r.t=0;return}var bs=n%this.DB;var cbs=this.DB-bs;var bm=(1<<bs)-1;r[0]=this[ds]>>bs;for(var i=ds+1;i<this.t;++i){r[i-ds-1]|=(this[i]&bm)<<cbs;r[i-ds]=this[i]>>bs}if(bs>0){r[this.t-ds-1]|=(this.s&bm)<<cbs}r.t=this.t-ds;r.clamp()}function bnpSubTo(a,r){var i=0,c=0,m=Math.min(a.t,this.t);while(i<m){c+=this[i]-a[i];r[i++]=c&this.DM;c>>=this.DB}if(a.t<this.t){c-=a.s;while(i<this.t){c+=this[i];r[i++]=c&this.DM;c>>=this.DB}c+=this.s}else{c+=this.s;while(i<a.t){c-=a[i];r[i++]=c&this.DM;c>>=this.DB}c-=a.s}r.s=(c<0)?-1:0;if(c<-1){r[i++]=this.DV+c}else{if(c>0){r[i++]=c}}r.t=i;r.clamp()}function bnpMultiplyTo(a,r){var x=this.abs(),y=a.abs();var i=x.t;r.t=i+y.t;while(--i>=0){r[i]=0}for(i=0;i<y.t;++i){r[i+x.t]=x.am(0,y[i],r,i,0,x.t)}r.s=0;r.clamp();if(this.s!=a.s){BigInteger.ZERO.subTo(r,r)}}function bnpSquareTo(r){var x=this.abs();var i=r.t=2*x.t;while(--i>=0){r[i]=0}for(i=0;i<x.t-1;++i){var c=x.am(i,x[i],r,2*i,0,1);if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1))>=x.DV){r[i+x.t]-=x.DV;r[i+x.t+1]=1}}if(r.t>0){r[r.t-1]+=x.am(i,x[i],r,2*i,0,1)}r.s=0;r.clamp()}function bnpDivRemTo(m,q,r){var pm=m.abs();if(pm.t<=0){return}var pt=this.abs();if(pt.t<pm.t){if(q!=null){q.fromInt(0)}if(r!=null){this.copyTo(r)}return}if(r==null){r=nbi()}var y=nbi(),ts=this.s,ms=m.s;var nsh=this.DB-nbits(pm[pm.t-1]);if(nsh>0){pm.lShiftTo(nsh,y);pt.lShiftTo(nsh,r)}else{pm.copyTo(y);pt.copyTo(r)}var ys=y.t;var y0=y[ys-1];if(y0==0){return}var yt=y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);var d1=this.FV/yt,d2=(1<<this.F1)/yt,e=1<<this.F2;var i=r.t,j=i-ys,t=(q==null)?nbi():q;y.dlShiftTo(j,t);if(r.compareTo(t)>=0){r[r.t++]=1;r.subTo(t,r)}BigInteger.ONE.dlShiftTo(ys,t);t.subTo(y,y);while(y.t<ys){y[y.t++]=0}while(--j>=0){var qd=(r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);if((r[i]+=y.am(0,qd,r,j,0,ys))<qd){y.dlShiftTo(j,t);r.subTo(t,r);while(r[i]<--qd){r.subTo(t,r)}}}if(q!=null){r.drShiftTo(ys,q);if(ts!=ms){BigInteger.ZERO.subTo(q,q)}}r.t=ys;r.clamp();if(nsh>0){r.rShiftTo(nsh,r)}if(ts<0){BigInteger.ZERO.subTo(r,r)}}function bnMod(a){var r=nbi();this.abs().divRemTo(a,null,r);if(this.s<0&&r.compareTo(BigInteger.ZERO)>0){a.subTo(r,r)}return r}function Classic(m){this.m=m}function cConvert(x){if(x.s<0||x.compareTo(this.m)>=0){return x.mod(this.m)}else{return x}}function cRevert(x){return x}function cReduce(x){x.divRemTo(this.m,null,x)}function cMulTo(x,y,r){x.multiplyTo(y,r);this.reduce(r)}function cSqrTo(x,r){x.squareTo(r);this.reduce(r)}Classic.prototype.convert=cConvert;Classic.prototype.revert=cRevert;Classic.prototype.reduce=cReduce;Classic.prototype.mulTo=cMulTo;Classic.prototype.sqrTo=cSqrTo;function bnpInvDigit(){if(this.t<1){return 0}var x=this[0];if((x&1)==0){return 0}var y=x&3;y=(y*(2-(x&15)*y))&15;y=(y*(2-(x&255)*y))&255;y=(y*(2-(((x&65535)*y)&65535)))&65535;y=(y*(2-x*y%this.DV))%this.DV;return(y>0)?this.DV-y:-y}function Montgomery(m){this.m=m;this.mp=m.invDigit();this.mpl=this.mp&32767;this.mph=this.mp>>15;this.um=(1<<(m.DB-15))-1;this.mt2=2*m.t}function montConvert(x){var r=nbi();x.abs().dlShiftTo(this.m.t,r);r.divRemTo(this.m,null,r);if(x.s<0&&r.compareTo(BigInteger.ZERO)>0){this.m.subTo(r,r)}return r}function montRevert(x){var r=nbi();x.copyTo(r);this.reduce(r);return r}function montReduce(x){while(x.t<=this.mt2){x[x.t++]=0}for(var i=0;i<this.m.t;++i){var j=x[i]&32767;var u0=(j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;j=i+this.m.t;x[j]+=this.m.am(0,u0,x,i,0,this.m.t);while(x[j]>=x.DV){x[j]-=x.DV;x[++j]++}}x.clamp();x.drShiftTo(this.m.t,x);if(x.compareTo(this.m)>=0){x.subTo(this.m,x)}}function montSqrTo(x,r){x.squareTo(r);this.reduce(r)}function montMulTo(x,y,r){x.multiplyTo(y,r);this.reduce(r)}Montgomery.prototype.convert=montConvert;Montgomery.prototype.revert=montRevert;Montgomery.prototype.reduce=montReduce;Montgomery.prototype.mulTo=montMulTo;Montgomery.prototype.sqrTo=montSqrTo;function bnpIsEven(){return((this.t>0)?(this[0]&1):this.s)==0}function bnpExp(e,z){if(e>4294967295||e<1){return BigInteger.ONE}var r=nbi(),r2=nbi(),g=z.convert(this),i=nbits(e)-1;g.copyTo(r);while(--i>=0){z.sqrTo(r,r2);if((e&(1<<i))>0){z.mulTo(r2,g,r)}else{var t=r;r=r2;r2=t}}return z.revert(r)}function bnModPowInt(e,m){var z;if(e<256||m.isEven()){z=new Classic(m)}else{z=new Montgomery(m)}return this.exp(e,z)}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);