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]);
	}
}