var dbits;var canary=244837814094590;var j_lm=((canary&16777215)==15715070);function BigInteger(e,d,f){if(e!=null){if("number"==typeof e){this.fromNumber(e,d,f)}else{if(d==null&&"string"!=typeof e){this.fromString(e,256)}else{this.fromString(e,d)}}}}function nbi(){return new BigInteger(null)}function am1(f,a,b,e,h,g){while(--g>=0){var d=a*this[f++]+b[e]+h;h=Math.floor(d/67108864);b[e++]=d&67108863}return h}function am2(f,q,r,e,o,a){var k=q&32767,p=q>>15;while(--a>=0){var d=this[f]&32767;var g=this[f++]>>15;var b=p*d+g*k;d=k*d+((b&32767)<<15)+r[e]+(o&1073741823);o=(d>>>30)+(b>>>15)+p*g+(o>>>30);r[e++]=d&1073741823}return o}function am3(f,q,r,e,o,a){var k=q&16383,p=q>>14;while(--a>=0){var d=this[f]&16383;var g=this[f++]>>14;var b=p*d+g*k;d=k*d+((b&16383)<<14)+r[e]+o;o=(d>>28)+(b>>14)+p*g;r[e++]=d&268435455}return o}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(a){return BI_RM.charAt(a)}function intAt(b,a){var d=BI_RC[b.charCodeAt(a)];return(d==null)?-1:d}function bnpCopyTo(b){for(var a=this.t-1;a>=0;--a){b[a]=this[a]}b.t=this.t;b.s=this.s}function bnpFromInt(a){this.t=1;this.s=(a<0)?-1:0;if(a>0){this[0]=a}else{if(a<-1){this[0]=a+DV}else{this.t=0}}}function nbv(a){var b=nbi();b.fromInt(a);return b}function bnpFromString(h,c){var e;if(c==16){e=4}else{if(c==8){e=3}else{if(c==256){e=8}else{if(c==2){e=1}else{if(c==32){e=5}else{if(c==4){e=2}else{this.fromRadix(h,c);return}}}}}}this.t=0;this.s=0;var g=h.length,d=false,f=0;while(--g>=0){var a=(e==8)?h[g]&255:intAt(h,g);if(a<0){if(h.charAt(g)=="-"){d=true}continue}d=false;if(f==0){this[this.t++]=a}else{if(f+e>this.DB){this[this.t-1]|=(a&((1<<(this.DB-f))-1))<<f;this[this.t++]=(a>>(this.DB-f))}else{this[this.t-1]|=a<<f}}f+=e;if(f>=this.DB){f-=this.DB}}if(e==8&&(h[0]&128)!=0){this.s=-1;if(f>0){this[this.t-1]|=((1<<(this.DB-f))-1)<<f}}this.clamp();if(d){BigInteger.ZERO.subTo(this,this)}}function bnpClamp(){var a=this.s&this.DM;while(this.t>0&&this[this.t-1]==a){--this.t}}function bnToString(c){if(this.s<0){return"-"+this.negate().toString(c)}var e;if(c==16){e=4}else{if(c==8){e=3}else{if(c==2){e=1}else{if(c==32){e=5}else{if(c==4){e=2}else{return this.toRadix(c)}}}}}var g=(1<<e)-1,l,a=false,h="",f=this.t;var j=this.DB-(f*this.DB)%e;if(f-->0){if(j<this.DB&&(l=this[f]>>j)>0){a=true;h=int2char(l)}while(f>=0){if(j<e){l=(this[f]&((1<<j)-1))<<(e-j);l|=this[--f]>>(j+=this.DB-e)}else{l=(this[f]>>(j-=e))&g;if(j<=0){j+=this.DB;--f}}if(l>0){a=true}if(a){h+=int2char(l)}}}return a?h:"0"}function bnNegate(){var a=nbi();BigInteger.ZERO.subTo(this,a);return a}function bnAbs(){return(this.s<0)?this.negate():this}function bnCompareTo(b){var d=this.s-b.s;if(d!=0){return d}var c=this.t;d=c-b.t;if(d!=0){return d}while(--c>=0){if((d=this[c]-b[c])!=0){return d}}return 0}function nbits(a){var c=1,b;if((b=a>>>16)!=0){a=b;c+=16}if((b=a>>8)!=0){a=b;c+=8}if((b=a>>4)!=0){a=b;c+=4}if((b=a>>2)!=0){a=b;c+=2}if((b=a>>1)!=0){a=b;c+=1}return c}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(c,b){var a;for(a=this.t-1;a>=0;--a){b[a+c]=this[a]}for(a=c-1;a>=0;--a){b[a]=0}b.t=this.t+c;b.s=this.s}function bnpDRShiftTo(c,b){for(var a=c;a<this.t;++a){b[a-c]=this[a]}b.t=Math.max(this.t-c,0);b.s=this.s}function bnpLShiftTo(j,e){var b=j%this.DB;var a=this.DB-b;var g=(1<<a)-1;var f=Math.floor(j/this.DB),h=(this.s<<b)&this.DM,d;for(d=this.t-1;d>=0;--d){e[d+f+1]=(this[d]>>a)|h;h=(this[d]&g)<<b}for(d=f-1;d>=0;--d){e[d]=0}e[f]=h;e.t=this.t+f+1;e.s=this.s;e.clamp()}function bnpRShiftTo(g,d){d.s=this.s;var e=Math.floor(g/this.DB);if(e>=this.t){d.t=0;return}var b=g%this.DB;var a=this.DB-b;var f=(1<<b)-1;d[0]=this[e]>>b;for(var c=e+1;c<this.t;++c){d[c-e-1]|=(this[c]&f)<<a;d[c-e]=this[c]>>b}if(b>0){d[this.t-e-1]|=(this.s&f)<<a}d.t=this.t-e;d.clamp()}function bnpSubTo(d,f){var e=0,g=0,b=Math.min(d.t,this.t);while(e<b){g+=this[e]-d[e];f[e++]=g&this.DM;g>>=this.DB}if(d.t<this.t){g-=d.s;while(e<this.t){g+=this[e];f[e++]=g&this.DM;g>>=this.DB}g+=this.s}else{g+=this.s;while(e<d.t){g-=d[e];f[e++]=g&this.DM;g>>=this.DB}g-=d.s}f.s=(g<0)?-1:0;if(g<-1){f[e++]=this.DV+g}else{if(g>0){f[e++]=g}}f.t=e;f.clamp()}function bnpMultiplyTo(c,e){var b=this.abs(),f=c.abs();var d=b.t;e.t=d+f.t;while(--d>=0){e[d]=0}for(d=0;d<f.t;++d){e[d+b.t]=b.am(0,f[d],e,d,0,b.t)}e.s=0;e.clamp();if(this.s!=c.s){BigInteger.ZERO.subTo(e,e)}}function bnpSquareTo(d){var a=this.abs();var b=d.t=2*a.t;while(--b>=0){d[b]=0}for(b=0;b<a.t-1;++b){var e=a.am(b,a[b],d,2*b,0,1);if((d[b+a.t]+=a.am(b+1,2*a[b],d,2*b+1,e,a.t-b-1))>=a.DV){d[b+a.t]-=a.DV;d[b+a.t+1]=1}}if(d.t>0){d[d.t-1]+=a.am(b,a[b],d,2*b,0,1)}d.s=0;d.clamp()}function bnpDivRemTo(n,h,g){var w=n.abs();if(w.t<=0){return}var k=this.abs();if(k.t<w.t){if(h!=null){h.fromInt(0)}if(g!=null){this.copyTo(g)}return}if(g==null){g=nbi()}var d=nbi(),a=this.s,l=n.s;var v=this.DB-nbits(w[w.t-1]);if(v>0){w.lShiftTo(v,d);k.lShiftTo(v,g)}else{w.copyTo(d);k.copyTo(g)}var p=d.t;var b=d[p-1];if(b==0){return}var o=b*(1<<this.F1)+((p>1)?d[p-2]>>this.F2:0);var A=this.FV/o,z=(1<<this.F1)/o,x=1<<this.F2;var u=g.t,s=u-p,f=(h==null)?nbi():h;d.dlShiftTo(s,f);if(g.compareTo(f)>=0){g[g.t++]=1;g.subTo(f,g)}BigInteger.ONE.dlShiftTo(p,f);f.subTo(d,d);while(d.t<p){d[d.t++]=0}while(--s>=0){var c=(g[--u]==b)?this.DM:Math.floor(g[u]*A+(g[u-1]+x)*z);if((g[u]+=d.am(0,c,g,s,0,p))<c){d.dlShiftTo(s,f);g.subTo(f,g);while(g[u]<--c){g.subTo(f,g)}}}if(h!=null){g.drShiftTo(p,h);if(a!=l){BigInteger.ZERO.subTo(h,h)}}g.t=p;g.clamp();if(v>0){g.rShiftTo(v,g)}if(a<0){BigInteger.ZERO.subTo(g,g)}}function bnMod(b){var c=nbi();this.abs().divRemTo(b,null,c);if(this.s<0&&c.compareTo(BigInteger.ZERO)>0){b.subTo(c,c)}return c}function Classic(a){this.m=a}function cConvert(a){if(a.s<0||a.compareTo(this.m)>=0){return a.mod(this.m)}else{return a}}function cRevert(a){return a}function cReduce(a){a.divRemTo(this.m,null,a)}function cMulTo(a,c,b){a.multiplyTo(c,b);this.reduce(b)}function cSqrTo(a,b){a.squareTo(b);this.reduce(b)}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 a=this[0];if((a&1)==0){return 0}var b=a&3;b=(b*(2-(a&15)*b))&15;b=(b*(2-(a&255)*b))&255;b=(b*(2-(((a&65535)*b)&65535)))&65535;b=(b*(2-a*b%this.DV))%this.DV;return(b>0)?this.DV-b:-b}function Montgomery(a){this.m=a;this.mp=a.invDigit();this.mpl=this.mp&32767;this.mph=this.mp>>15;this.um=(1<<(a.DB-15))-1;this.mt2=2*a.t}function montConvert(a){var b=nbi();a.abs().dlShiftTo(this.m.t,b);b.divRemTo(this.m,null,b);if(a.s<0&&b.compareTo(BigInteger.ZERO)>0){this.m.subTo(b,b)}return b}function montRevert(a){var b=nbi();a.copyTo(b);this.reduce(b);return b}function montReduce(a){while(a.t<=this.mt2){a[a.t++]=0}for(var c=0;c<this.m.t;++c){var b=a[c]&32767;var d=(b*this.mpl+(((b*this.mph+(a[c]>>15)*this.mpl)&this.um)<<15))&a.DM;b=c+this.m.t;a[b]+=this.m.am(0,d,a,c,0,this.m.t);while(a[b]>=a.DV){a[b]-=a.DV;a[++b]++}}a.clamp();a.drShiftTo(this.m.t,a);if(a.compareTo(this.m)>=0){a.subTo(this.m,a)}}function montSqrTo(a,b){a.squareTo(b);this.reduce(b)}function montMulTo(a,c,b){a.multiplyTo(c,b);this.reduce(b)}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(h,j){if(h>4294967295||h<1){return BigInteger.ONE}var f=nbi(),a=nbi(),d=j.convert(this),c=nbits(h)-1;d.copyTo(f);while(--c>=0){j.sqrTo(f,a);if((h&(1<<c))>0){j.mulTo(a,d,f)}else{var b=f;f=a;a=b}}return j.revert(f)}function bnModPowInt(b,a){var c;if(b<256||a.isEven()){c=new Classic(a)}else{c=new Montgomery(a)}return this.exp(b,c)}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);function bnClone(){var a=nbi();this.copyTo(a);return a}function bnIntValue(){if(this.s<0){if(this.t==1){return this[0]-this.DV}else{if(this.t==0){return -1}}}else{if(this.t==1){return this[0]}else{if(this.t==0){return 0}}}return((this[1]&((1<<(32-this.DB))-1))<<this.DB)|this[0]}function bnByteValue(){return(this.t==0)?this.s:(this[0]<<24)>>24}function bnShortValue(){return(this.t==0)?this.s:(this[0]<<16)>>16}function bnpChunkSize(a){return Math.floor(Math.LN2*this.DB/Math.log(a))}function bnSigNum(){if(this.s<0){return -1}else{if(this.t<=0||(this.t==1&&this[0]<=0)){return 0}else{return 1}}}function bnpToRadix(c){if(c==null){c=10}if(this.signum()==0||c<2||c>36){return"0"}var f=this.chunkSize(c);var e=Math.pow(c,f);var i=nbv(e),j=nbi(),h=nbi(),g="";this.divRemTo(i,j,h);while(j.signum()>0){g=(e+h.intValue()).toString(c).substr(1)+g;j.divRemTo(i,j,h)}return h.intValue().toString(c)+g}function bnpFromRadix(m,h){this.fromInt(0);if(h==null){h=10}var f=this.chunkSize(h);var g=Math.pow(h,f),e=false,a=0,l=0;for(var c=0;c<m.length;++c){var k=intAt(m,c);if(k<0){if(m.charAt(c)=="-"&&this.signum()==0){e=true}continue}l=h*l+k;if(++a>=f){this.dMultiply(g);this.dAddOffset(l,0);a=0;l=0}}if(a>0){this.dMultiply(Math.pow(h,a));this.dAddOffset(l,0)}if(e){BigInteger.ZERO.subTo(this,this)}}function bnpFromNumber(f,e,h){if("number"==typeof e){if(f<2){this.fromInt(1)}else{this.fromNumber(f,h);if(!this.testBit(f-1)){this.bitwiseTo(BigInteger.ONE.shiftLeft(f-1),op_or,this)}if(this.isEven()){this.dAddOffset(1,0)}while(!this.isProbablePrime(e)){this.dAddOffset(2,0);if(this.bitLength()>f){this.subTo(BigInteger.ONE.shiftLeft(f-1),this)}}}}else{var d=new Array(),g=f&7;d.length=(f>>3)+1;e.nextBytes(d);if(g>0){d[0]&=((1<<g)-1)}else{d[0]=0}this.fromString(d,256)}}function bnToByteArray(){var b=this.t,c=new Array();c[0]=this.s;var e=this.DB-(b*this.DB)%8,f,a=0;if(b-->0){if(e<this.DB&&(f=this[b]>>e)!=(this.s&this.DM)>>e){c[a++]=f|(this.s<<(this.DB-e))}while(b>=0){if(e<8){f=(this[b]&((1<<e)-1))<<(8-e);f|=this[--b]>>(e+=this.DB-8)}else{f=(this[b]>>(e-=8))&255;if(e<=0){e+=this.DB;--b}}if((f&128)!=0){f|=-256}if(a==0&&(this.s&128)!=(f&128)){++a}if(a>0||f!=this.s){c[a++]=f}}}return c}function bnEquals(b){return(this.compareTo(b)==0)}function bnMin(b){return(this.compareTo(b)<0)?this:b}function bnMax(b){return(this.compareTo(b)>0)?this:b}function bnpBitwiseTo(c,h,e){var d,g,b=Math.min(c.t,this.t);for(d=0;d<b;++d){e[d]=h(this[d],c[d])}if(c.t<this.t){g=c.s&this.DM;for(d=b;d<this.t;++d){e[d]=h(this[d],g)}e.t=this.t}else{g=this.s&this.DM;for(d=b;d<c.t;++d){e[d]=h(g,c[d])}e.t=c.t}e.s=h(this.s,c.s);e.clamp()}function op_and(a,b){return a&b}function bnAnd(b){var c=nbi();this.bitwiseTo(b,op_and,c);return c}function op_or(a,b){return a|b}function bnOr(b){var c=nbi();this.bitwiseTo(b,op_or,c);return c}function op_xor(a,b){return a^b}function bnXor(b){var c=nbi();this.bitwiseTo(b,op_xor,c);return c}function op_andnot(a,b){return a&~b}function bnAndNot(b){var c=nbi();this.bitwiseTo(b,op_andnot,c);return c}function bnNot(){var b=nbi();for(var a=0;a<this.t;++a){b[a]=this.DM&~this[a]}b.t=this.t;b.s=~this.s;return b}function bnShiftLeft(b){var a=nbi();if(b<0){this.rShiftTo(-b,a)}else{this.lShiftTo(b,a)}return a}function bnShiftRight(b){var a=nbi();if(b<0){this.lShiftTo(-b,a)}else{this.rShiftTo(b,a)}return a}function lbit(a){if(a==0){return -1}var b=0;if((a&65535)==0){a>>=16;b+=16}if((a&255)==0){a>>=8;b+=8}if((a&15)==0){a>>=4;b+=4}if((a&3)==0){a>>=2;b+=2}if((a&1)==0){++b}return b}function bnGetLowestSetBit(){for(var a=0;a<this.t;++a){if(this[a]!=0){return a*this.DB+lbit(this[a])}}if(this.s<0){return this.t*this.DB}return -1}function cbit(a){var b=0;while(a!=0){a&=a-1;++b}return b}function bnBitCount(){var c=0,a=this.s&this.DM;for(var b=0;b<this.t;++b){c+=cbit(this[b]^a)}return c}function bnTestBit(b){var a=Math.floor(b/this.DB);if(a>=this.t){return(this.s!=0)}return((this[a]&(1<<(b%this.DB)))!=0)}function bnpChangeBit(c,b){var a=BigInteger.ONE.shiftLeft(c);this.bitwiseTo(a,b,a);return a}function bnSetBit(a){return this.changeBit(a,op_or)}function bnClearBit(a){return this.changeBit(a,op_andnot)}function bnFlipBit(a){return this.changeBit(a,op_xor)}function bnpAddTo(d,f){var e=0,g=0,b=Math.min(d.t,this.t);while(e<b){g+=this[e]+d[e];f[e++]=g&this.DM;g>>=this.DB}if(d.t<this.t){g+=d.s;while(e<this.t){g+=this[e];f[e++]=g&this.DM;g>>=this.DB}g+=this.s}else{g+=this.s;while(e<d.t){g+=d[e];f[e++]=g&this.DM;g>>=this.DB}g+=d.s}f.s=(g<0)?-1:0;if(g>0){f[e++]=g}else{if(g<-1){f[e++]=this.DV+g}}f.t=e;f.clamp()}function bnAdd(b){var c=nbi();this.addTo(b,c);return c}function bnSubtract(b){var c=nbi();this.subTo(b,c);return c}function bnMultiply(b){var c=nbi();this.multiplyTo(b,c);return c}function bnDivide(b){var c=nbi();this.divRemTo(b,c,null);return c}function bnRemainder(b){var c=nbi();this.divRemTo(b,null,c);return c}function bnDivideAndRemainder(b){var d=nbi(),c=nbi();this.divRemTo(b,d,c);return new Array(d,c)}function bnpDMultiply(a){this[this.t]=this.am(0,a-1,this,0,0,this.t);++this.t;this.clamp()}function bnpDAddOffset(b,a){while(this.t<=a){this[this.t++]=0}this[a]+=b;while(this[a]>=this.DV){this[a]-=this.DV;if(++a>=this.t){this[this.t++]=0}++this[a]}}function NullExp(){}function nNop(a){return a}function nMulTo(a,c,b){a.multiplyTo(c,b)}function nSqrTo(a,b){a.squareTo(b)}NullExp.prototype.convert=nNop;NullExp.prototype.revert=nNop;NullExp.prototype.mulTo=nMulTo;NullExp.prototype.sqrTo=nSqrTo;function bnPow(a){return this.exp(a,new NullExp())}function bnpMultiplyLowerTo(b,f,e){var d=Math.min(this.t+b.t,f);e.s=0;e.t=d;while(d>0){e[--d]=0}var c;for(c=e.t-this.t;d<c;++d){e[d+this.t]=this.am(0,b[d],e,d,0,this.t)}for(c=Math.min(b.t,f);d<c;++d){this.am(0,b[d],e,d,0,f-d)}e.clamp()}function bnpMultiplyUpperTo(b,e,d){--e;var c=d.t=this.t+b.t-e;d.s=0;while(--c>=0){d[c]=0}for(c=Math.max(e-this.t,0);c<b.t;++c){d[this.t+c-e]=this.am(e-c,b[c],d,0,0,this.t+c-e)}d.clamp();d.drShiftTo(1,d)}function Barrett(a){this.r2=nbi();this.q3=nbi();BigInteger.ONE.dlShiftTo(2*a.t,this.r2);this.mu=this.r2.divide(a);this.m=a}function barrettConvert(a){if(a.s<0||a.t>2*this.m.t){return a.mod(this.m)}else{if(a.compareTo(this.m)<0){return a}else{var b=nbi();a.copyTo(b);this.reduce(b);return b}}}function barrettRevert(a){return a}function barrettReduce(a){a.drShiftTo(this.m.t-1,this.r2);if(a.t>this.m.t+1){a.t=this.m.t+1;a.clamp()}this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);while(a.compareTo(this.r2)<0){a.dAddOffset(1,this.m.t+1)}a.subTo(this.r2,a);while(a.compareTo(this.m)>=0){a.subTo(this.m,a)}}function barrettSqrTo(a,b){a.squareTo(b);this.reduce(b)}function barrettMulTo(a,c,b){a.multiplyTo(c,b);this.reduce(b)}Barrett.prototype.convert=barrettConvert;Barrett.prototype.revert=barrettRevert;Barrett.prototype.reduce=barrettReduce;Barrett.prototype.mulTo=barrettMulTo;Barrett.prototype.sqrTo=barrettSqrTo;function bnModPow(q,f){var o=q.bitLength(),h,b=nbv(1),v;if(o<=0){return b}else{if(o<18){h=1}else{if(o<48){h=3}else{if(o<144){h=4}else{if(o<768){h=5}else{h=6}}}}}if(o<8){v=new Classic(f)}else{if(f.isEven()){v=new Barrett(f)}else{v=new Montgomery(f)}}var p=new Array(),d=3,s=h-1,a=(1<<h)-1;p[1]=v.convert(this);if(h>1){var A=nbi();v.sqrTo(p[1],A);while(d<=a){p[d]=nbi();v.mulTo(A,p[d-2],p[d]);d+=2}}var l=q.t-1,x,u=true,c=nbi(),y;o=nbits(q[l])-1;while(l>=0){if(o>=s){x=(q[l]>>(o-s))&a}else{x=(q[l]&((1<<(o+1))-1))<<(s-o);if(l>0){x|=q[l-1]>>(this.DB+o-s)}}d=h;while((x&1)==0){x>>=1;--d}if((o-=d)<0){o+=this.DB;--l}if(u){p[x].copyTo(b);u=false}else{while(d>1){v.sqrTo(b,c);v.sqrTo(c,b);d-=2}if(d>0){v.sqrTo(b,c)}else{y=b;b=c;c=y}v.mulTo(c,p[x],b)}while(l>=0&&(q[l]&(1<<o))==0){v.sqrTo(b,c);y=b;b=c;c=y;if(--o<0){o=this.DB-1;--l}}}return v.revert(b)}function bnGCD(c){var b=(this.s<0)?this.negate():this.clone();var h=(c.s<0)?c.negate():c.clone();if(b.compareTo(h)<0){var e=b;b=h;h=e}var d=b.getLowestSetBit(),f=h.getLowestSetBit();if(f<0){return b}if(d<f){f=d}if(f>0){b.rShiftTo(f,b);h.rShiftTo(f,h)}while(b.signum()>0){if((d=b.getLowestSetBit())>0){b.rShiftTo(d,b)}if((d=h.getLowestSetBit())>0){h.rShiftTo(d,h)}if(b.compareTo(h)>=0){b.subTo(h,b);b.rShiftTo(1,b)}else{h.subTo(b,h);h.rShiftTo(1,h)}}if(f>0){h.lShiftTo(f,h)}return h}function bnpModInt(e){if(e<=0){return 0}var c=this.DV%e,b=(this.s<0)?e-1:0;if(this.t>0){if(c==0){b=this[0]%e}else{for(var a=this.t-1;a>=0;--a){b=(c*b+this[a])%e}}}return b}function bnModInverse(f){var j=f.isEven();if((this.isEven()&&j)||f.signum()==0){return BigInteger.ZERO}var i=f.clone(),h=this.clone();var g=nbv(1),e=nbv(0),l=nbv(0),k=nbv(1);while(i.signum()!=0){while(i.isEven()){i.rShiftTo(1,i);if(j){if(!g.isEven()||!e.isEven()){g.addTo(this,g);e.subTo(f,e)}g.rShiftTo(1,g)}else{if(!e.isEven()){e.subTo(f,e)}}e.rShiftTo(1,e)}while(h.isEven()){h.rShiftTo(1,h);if(j){if(!l.isEven()||!k.isEven()){l.addTo(this,l);k.subTo(f,k)}l.rShiftTo(1,l)}else{if(!k.isEven()){k.subTo(f,k)}}k.rShiftTo(1,k)}if(i.compareTo(h)>=0){i.subTo(h,i);if(j){g.subTo(l,g)}e.subTo(k,e)}else{h.subTo(i,h);if(j){l.subTo(g,l)}k.subTo(e,k)}}if(h.compareTo(BigInteger.ONE)!=0){return BigInteger.ZERO}if(k.compareTo(f)>=0){return k.subtract(f)}if(k.signum()<0){k.addTo(f,k)}else{return k}if(k.signum()<0){return k.add(f)}else{return k}}var lowprimes=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];var lplim=(1<<26)/lowprimes[lowprimes.length-1];function bnIsProbablePrime(e){var d,b=this.abs();if(b.t==1&&b[0]<=lowprimes[lowprimes.length-1]){for(d=0;d<lowprimes.length;++d){if(b[0]==lowprimes[d]){return true}}return false}if(b.isEven()){return false}d=1;while(d<lowprimes.length){var a=lowprimes[d],c=d+1;while(c<lowprimes.length&&a<lplim){a*=lowprimes[c++]}a=b.modInt(a);while(d<c){if(a%lowprimes[d++]==0){return false}}}return b.millerRabin(e)}function bnpMillerRabin(f){var g=this.subtract(BigInteger.ONE);var c=g.getLowestSetBit();if(c<=0){return false}var h=g.shiftRight(c);f=(f+1)>>1;if(f>lowprimes.length){f=lowprimes.length}var b=nbi();for(var e=0;e<f;++e){b.fromInt(lowprimes[e]);var l=b.modPow(h,this);if(l.compareTo(BigInteger.ONE)!=0&&l.compareTo(g)!=0){var d=1;while(d++<c&&l.compareTo(g)!=0){l=l.modPowInt(2,this);if(l.compareTo(BigInteger.ONE)==0){return false}}if(l.compareTo(g)!=0){return false}}}return true}BigInteger.prototype.chunkSize=bnpChunkSize;BigInteger.prototype.toRadix=bnpToRadix;BigInteger.prototype.fromRadix=bnpFromRadix;BigInteger.prototype.fromNumber=bnpFromNumber;BigInteger.prototype.bitwiseTo=bnpBitwiseTo;BigInteger.prototype.changeBit=bnpChangeBit;BigInteger.prototype.addTo=bnpAddTo;BigInteger.prototype.dMultiply=bnpDMultiply;BigInteger.prototype.dAddOffset=bnpDAddOffset;BigInteger.prototype.multiplyLowerTo=bnpMultiplyLowerTo;BigInteger.prototype.multiplyUpperTo=bnpMultiplyUpperTo;BigInteger.prototype.modInt=bnpModInt;BigInteger.prototype.millerRabin=bnpMillerRabin;BigInteger.prototype.clone=bnClone;BigInteger.prototype.intValue=bnIntValue;BigInteger.prototype.byteValue=bnByteValue;BigInteger.prototype.shortValue=bnShortValue;BigInteger.prototype.signum=bnSigNum;BigInteger.prototype.toByteArray=bnToByteArray;BigInteger.prototype.equals=bnEquals;BigInteger.prototype.min=bnMin;BigInteger.prototype.max=bnMax;BigInteger.prototype.and=bnAnd;BigInteger.prototype.or=bnOr;BigInteger.prototype.xor=bnXor;BigInteger.prototype.andNot=bnAndNot;BigInteger.prototype.not=bnNot;BigInteger.prototype.shiftLeft=bnShiftLeft;BigInteger.prototype.shiftRight=bnShiftRight;BigInteger.prototype.getLowestSetBit=bnGetLowestSetBit;BigInteger.prototype.bitCount=bnBitCount;BigInteger.prototype.testBit=bnTestBit;BigInteger.prototype.setBit=bnSetBit;BigInteger.prototype.clearBit=bnClearBit;BigInteger.prototype.flipBit=bnFlipBit;BigInteger.prototype.add=bnAdd;BigInteger.prototype.subtract=bnSubtract;BigInteger.prototype.multiply=bnMultiply;BigInteger.prototype.divide=bnDivide;BigInteger.prototype.remainder=bnRemainder;BigInteger.prototype.divideAndRemainder=bnDivideAndRemainder;BigInteger.prototype.modPow=bnModPow;BigInteger.prototype.modInverse=bnModInverse;BigInteger.prototype.pow=bnPow;BigInteger.prototype.gcd=bnGCD;BigInteger.prototype.isProbablePrime=bnIsProbablePrime; 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