#include #define rep(i,n) for(int i=0;i<(n);i++) using namespace std; class bint{ static const int BASE=1000000000; int sign; vector a; bint& normalize(){ while(!a.empty() && a.back()==0) a.pop_back(); if(a.empty()) sign=1; return *this; } public: bint(long long v=0){ *this=v; } bint(const string& s){ *this=s; } bint& operator=(long long v){ if(v>=0) sign=1; else sign=-1, v*=-1; a.clear(); for(;v>0;v/=BASE) a.emplace_back(v%BASE); return *this; } bint& operator=(const string& s){ int n=s.length(),t=0; sign=1; if (s[0]=='+') t++; else if(s[0]=='-') t++, sign=-1; a.clear(); for(int i=n;i>t;i-=9) a.emplace_back(stoi(s.substr(max(i-9,t),i-max(i-9,t)))); return normalize(); } bint& operator+=(const bint& b){ int m=a.size(),n=b.a.size(),carry=0; if(sign==b.sign){ if(m=BASE) a[i]-=BASE, carry=1; else carry=0; } for(int i=n;carry>0;i++){ if(a.size()==i) a.resize(i+1); a[i]+=carry; if(a[i]>=BASE) a[i]-=BASE, carry=1; else carry=0; } } else if(abs(*this)>=abs(b)){ rep(i,n){ a[i]-=b.a[i]+carry; if(a[i]<0) a[i]+=BASE, carry=1; else carry=0; } for(int i=n;carry>0;i++){ a[i]-=carry; if(a[i]<0) a[i]+=BASE, carry=1; else carry=0; } } else{ a.resize(n); rep(i,n){ a[i]=b.a[i]-(a[i]+carry); if(a[i]<0) a[i]+=BASE, carry=1; else carry=0; } sign*=-1; } return normalize(); } bint& operator-=(const bint& b){ sign*=-1; *this+=b; sign*=-1; return normalize(); } bint& operator*=(int v){ if(v<0) sign*=-1, v=-v; int n=a.size(),carry=0; rep(i,n){ auto tmp=(long long)a[i]*v+carry; a[i]=tmp%BASE; carry=tmp/BASE; } if(carry>0) a.emplace_back(carry); return normalize(); } bint& operator/=(int v){ if(v<0) sign*=-1, v*=-1; for(int i=a.size()-1,rem=0;i>=0;i--){ auto tmp=a[i]+(long long)rem*BASE; a[i]=tmp/v; rem=tmp%v; } return normalize(); } bint& operator*=(const long long& v){ return *this=(*this)*bint(v); } bint& operator/=(const long long& v){ return *this=(*this)/bint(v); } bint& operator*=(const bint& b){ return *this=(*this)*b; } bint& operator/=(const bint& b){ return *this=(*this)/b; } bint& operator%=(const bint& b){ return *this=(*this)%b; } bint operator+(const bint& b)const{ return bint(*this)+=b; } bint operator-(const bint& b)const{ return bint(*this)-=b; } bint operator*(int v)const{ return bint(*this)*=v; } bint operator/(int v)const{ return bint(*this)/=v; } bint operator*(const long long& v)const{ return bint(*this)*=bint(v); } bint operator/(const long long& v)const{ return bint(*this)/=bint(v); } bint operator*(const bint& b)const{ int m=a.size(),n=b.a.size(); if(m==0 || n==0) return 0; bint res; res.a.resize(m+n); rep(i,m) rep(j,n) { auto tmp=(long long)a[i]*b.a[j]; res.a[i+j]+=tmp%BASE; if(tmp>=BASE) res.a[i+j+1]+=tmp/BASE; for(int k=0;;k++){ if(k>0 && res.a[i+j+k]=BASE){ res.a[i+j+k]-=BASE; res.a[i+j+k+1]++; } } } res.sign=sign*b.sign; return res.normalize(); } bint operator/(const bint& b)const{ return divmod(*this,b).first; } bint operator%(const bint& b)const{ return divmod(*this,b).second; } bint operator-()const{ bint res=*this; if(res!=0) res.sign*=-1; return res; } bool operator< (const bint& b)const{ if(sign!=b.sign) return signn; for(int i=m-1;i>=0;i--) if(a[i]!=b.a[i]) return sign==1?a[i]b.a[i]; return false; } bool operator> (const bint& b)const{ return b<(*this); } bool operator<=(const bint& b)const{ return !(b<(*this)); } bool operator>=(const bint& b)const{ return !((*this)>(istream& is,bint& b){ string s; is>>s; b=bint(s); return is; } friend ostream& operator<<(ostream& os,const bint& b){ if(b.sign==-1) os<<'-'; os<<(b.a.empty()?0:b.a.back()); for(int i=b.a.size()-2;i>=0;i--) os< divmod(const bint& a1,const bint& b1){ int norm=BASE/(b1.a.back()+1); bint a=abs(a1)*norm,b=abs(b1)*norm,q,r; q.a.resize(a.a.size()); for(int i=a.a.size()-1;i>=0;i--){ r*=BASE; r+=a.a[i]; int s1=(r.a.size()<=b.a.size()?0:r.a[b.a.size()]); int s2=(r.a.size()<=b.a.size()-1?0:r.a[b.a.size()-1]); int d=((long long)BASE*s1+s2)/b.a.back(); r-=b*d; while(r<0) r+=b, d--; q.a[i]=d; } q.sign=a1.sign*b1.sign; r.sign=a1.sign; return make_pair(q.normalize(),r.normalize()/norm); } }; string to_string(const bint& b){ stringstream ss; ss<>a>>b; rep(i,50) a*=10; string s=to_string(a/b); int len=s.length(); s=s.substr(0,len-50)+"."+s.substr(len-50); if(s[0]=='.') s="0"+s; cout<