/*! (c) Tom Wu | http://www-cs-students.stanford.edu/~tjw/jsbn/
 */
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 bnSquare(){var a=nbi();this.squareTo(a);return a}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){if(b==0){return}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=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997];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[Math.floor(Math.random()*lowprimes.length)]);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;BigInteger.prototype.square=bnSquare;