高精度模板

namespace LONGER{
    typedef long long ll;
    typedef unsigned long long UTYPE;
    typedef ll TYPE;
    const TYPE sll=sizeof(TYPE);
    const TYPE MAXLENGTH=50;
    inline TYPE max(const TYPE&a,const TYPE&b){return a<b?b:a;}
    inline void Swap(long long &a,long long &b){a=a^b;b=a^b;a=a^b;}
    struct Longer{
    #define LOWBIT 1000000000
        int size;
        TYPE num[MAXLENGTH];
        Longer(const TYPE&a=0){size=1;memset(num,0,sizeof(num));num[1]=a;}
        TYPE &operator[](int x){return num[x];}
    };
    Longer operator +(const Longer&,const Longer&);
    Longer operator -(const Longer&,const Longer&);
    Longer operator *(const Longer&,const Longer&);
    Longer operator /(const Longer&,const Longer&);
    Longer operator /(const Longer&,const TYPE&);
    Longer operator % (const Longer&,const Longer&);
    Longer operator <<(const Longer&,const TYPE&);
    Longer operator >>(const Longer&,const TYPE&);
    bool   operator <(const Longer&,const Longer&);
    bool   operator >(const Longer&,const Longer&);
    bool   operator >=(const Longer&,const Longer&);
    bool   operator <=(const Longer&,const Longer&);
    bool   operator !=(const Longer&,const Longer&);
    bool   operator ==(const Longer&,const Longer&);
    void read(Longer &);
    void fread(Longer &,FILE*);
    void put(const Longer&);
    void fput(const Longer&,FILE*);
    Longer exchange(const Longer&);
    Longer exchange(const Longer&a){
        Longer c;
        c.size=a.size;
        for(int i=1;i<=a.size;++i)
            c.num[i]=a.num[a.size-i+1];
        return c;
    }
    Longer operator <<(const Longer&a,const TYPE&b){
        Longer c;
        c.size=a.size+b;
        for(int i=1;i<=a.size;++i)
            if( i+b <MAXLENGTH )c.num[i+b]=a.num[i];
        return c;
    }
    Longer operator >>(const Longer&a,const TYPE&b){
        Longer c;
        c.size=max(1,a.size-b);
        for(int i=b+1;i<=a.size;++i)
            c.num[i-b]=a.num[i];
        return c;
    }
    Longer operator +(const Longer &a,const Longer &b){
        Longer c;
        c.size=max(a.size,b.size);
        for(int i=1;i<=c.size;++i)
            c.num[i]=a.num[i]+b.num[i];
        for(int i=1;i<=c.size;++i){
            c.num[i+1]+=c.num[i]/LOWBIT;
            c.num[i]%=LOWBIT;
        }
        while(c.num[c.size+1]!=0)c.size++;
        return c;
    }
    Longer operator -(const Longer &a,const Longer &b){
        if(a<b)return 0;
        Longer c;
        c.size=max(a.size,b.size);
        for(int i=1;i<=c.size;++i)
            c.num[i]=a.num[i]-b.num[i];
        for(int i=1;i<=c.size;++i)
            if(c.num[i]<0){
                c.num[i]+=LOWBIT;
                --c.num[i+1];
            }
        while(c.num[c.size]==0&&c.size>0)--c.size;
        return c;
    }
    Longer operator *(const Longer &a,const Longer &b){
        Longer c;
        c.size=a.size+b.size-1;
        for(int i=1;i<=a.size;++i)
            for(int j=1;j<=b.size;++j)
                c.num[i+j-1]+=a.num[i]*b.num[j];
        for(int i=1;i<=c.size;++i){
            c.num[i+1]+=c.num[i]/LOWBIT;
            c.num[i]%=LOWBIT;
        }
        if(c.num[c.size+1]!=0)c.size++;
        return c;
    }
    Longer operator / (const Longer&a,const TYPE&b){
        if(b==1)return a;
        TYPE d=0;
        Longer c;
        c.size=a.size;
        for(int i=c.size;i>=1;--i){
            c.num[i]=(d*LOWBIT+a.num[i])/b;
            d=(d*LOWBIT+a.num[i])%b;
        }
        while(c.num[c.size]==0&&c.size>0)--c.size;
        return c;
    }
    Longer operator / (const Longer &_a,const Longer &_b){
        if(_b==1)return _a;
        Longer l=1,r=1,mid,p,a=_a,b=_b;
        if(b==0){printf("Runtime Error in Big Integer :: the devided number cannot be zero.\n");abort();}
        if(a==0||a<b)return 0;
        TYPE k=max(a.size-b.size,0);
        l=l<<(k-1);
        r=r<<(k+1);
        //put(l);put(r);
        while(l<r){
            mid=((l+r)/2);
            p=mid*b;
            if(p==a)return mid;
            else if(p>a)r=mid+(-1);
                 else l=mid+1;
        }
        if(l*b>a)return l-1;
        return l;
    }
    Longer operator %(const Longer &_a,const Longer&_b){
        return _a-(_a/_b)*_b;
    }
    bool operator <(const Longer&a,const Longer&b){
        if(a.size!=b.size)return a.size<b.size;
        for(int i=a.size;i>=1;--i)
            if(a.num[i]!=b.num[i])
            return a.num[i]<b.num[i];
        return 0;
    }
    bool operator >(const Longer&a,const Longer&b){return b<a;}
    bool operator >=(const Longer&a,const Longer&b){return a>b||a==b;}
    bool operator <=(const Longer&a,const Longer&b){return a<b||a==b;}
    bool operator !=(const Longer&a,const Longer&b){return !(a==b);}
    bool operator ==(const Longer &a,const Longer&b){return !(a<b)&&!(b<a);}
    void read(Longer &t){t=0;
        std::string s;
        char str[1024];
        scanf("%s",str);
        s=str;
        int sizen=s.length();
    //  printf("\n\nsizen->%d\n\n",sizen);
        int p=sizen%9,i=0;TYPE k=0;
        t.size=sizen/9+(sizen%9!=0);
        if(p!=0){for(i=0;i<p;++i)k=k*10+s[i]-'0'; t.num[t.size--]=k; k=0;}
        while(t.size){
            p=i+9;
            for(;i<p;++i)k=k*10+s[i]-'0';
            t.num[t.size--]=k;k=0;
        }t.size=sizen/9+(sizen%9!=0);
        t=t+0;
    }
    void put(const Longer &k){
        printf("%lld",k.num[k.size]);
        for(int i=k.size-1;i>=1;--i)
            printf("%.9lld",k.num[i]);
    }
    void fread(Longer &t,FILE*IR){t=0;
        std::string s;
        char str[1024];
        fscanf(IR,"%s",str);
        s=str;
        int sizen=s.length();
        int p=sizen%9,i=0;TYPE k=0;
        t.size=sizen/9+(sizen%9!=0);
        if(p!=0){for(i=0;i<p;++i)k=k*10+s[i]-'0'; t.num[t.size--]=k; k=0;}
        while(t.size){
            p=i+9;
            for(;i<p;++i)k=k*10+s[i]-'0';
            t.num[t.size--]=k;k=0;
        }t.size=sizen/9+(sizen%9!=0);
        t=t+0;
    }
    void fput(const Longer &k,FILE*OR){
        fprintf(OR,"%lld",k.num[k.size]);
        for(int i=k.size-1;i>=1;--i)
            fprintf(OR,"%09lld",k.num[i]);
    }
}