K-fold interval prefix sum

K-fold interval prefix sum

One-dimensional difference explanation

#include<iostream>


using namespace std;

#define  ll long long

int a[100005];

ll sum[100005];

ll res[100005];

ll ans;
int main()
{
    
    
	int n,k; 
	
	scanf("%d%d",&n,&k);
	
	for(int i=1;i<=n;i++)
	{
    
    
		scanf("%d",&a[i]);
	}
	
	sum[0]=0;
	
	res[sum[0]]++; //注意加上了个a[0]=0 如果区别 1-3满足 则sum[0]%k==sum[3]%k
	
	for(int i=1;i<=n;i++)
	{
    
    
		sum[i]=(sum[i-1]+a[i])%k;
		
		res[sum[i]]++;
	}
	
	for(int i=0;i<k;i++)
	{
    
    
		ans+=(res[i]*(res[i]-1))/2;
	}
	
	printf("%lld",ans);
}