x=a%pq与x=a%p,x=a%q的关系(pq互质)

http://prayer.hustoj.com/problem.php?id=1770
我们 口胡 证明一下；
a%p=a%q=x;
tp+x=a=t’q+x;
∴tp=t’q;
∵(p,q)==1;
所以
tp=t’q;
即
kqp=k’pq=tp=t’q;
kqp+x=a;
a%(qp)=x;

#include<iostream>
#include<cstdio>
#include<cstring>
#define Ll long long
using namespace std;
const Ll NN=1e8;
const int N=8;
struct H{Ll a[1250],len;H(){memset(a,0,sizeof a);len=1;}void clear(){memset(a,0,sizeof a);len=1;}
};
void init(H &a){string s; cin>>s; int l; a.len=0;for(int r=s.length()-1;r>=0;r-=N){a.a[++a.len]=0;           if(r>=N-1)l=r-N+1;else l=0;for(int i=l;i<=r;i++)a.a[a.len]=a.a[a.len]*10+s[i]-48;}
}  
void outit(H a){printf("%lld",a.a[a.len]);for(int i=a.len-1;i;i--){for(int k=NN/10;a.a[i]<k;k/=10)printf("0");if(a.a[i])printf("%lld",a.a[i]); }printf("\n");  
}
int main()
{H s;init(s);outit(s);
}