#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int N=5000005;
ll n,m;
map<ll,ll>sq;
ll sum[N]={0};
ll a[N];
int main(){
	ll ans=0;
	cin>>n>>m;
	for(int i=1;i<=n;i++){
		cin>>a[i];
		sum[i]=sum[i-1]+a[i];
		
	}
	for(int i=1;i<=n;i++){
		sum[i]=(sum[i]-i%m+m)%m;
		
	}
	ll mn=min(m-1,n);
	for(int i=0;i<=mn;i++){
		ans+=sq[sum[i]];
		sq[sum[i]]++;
	}
	for(int i=mn+1;i<=n;i++)
    {
        sq[sum[i-m]]--;
        ans+=sq[sum[i]];
        sq[sum[i]]++;
    }	
	cout<<ans<<endl;
	return 0;
} 
### Prompt

Your challenge is to write a cpp solution to the following problem:

Given are a sequence of N positive integers A_1, A_2, \ldots, A_N, and a positive integer K.

Find the number of non-empty contiguous subsequences in A such that the remainder when dividing the sum of its elements by K is equal to the number of its elements. We consider two subsequences different if they are taken from different positions, even if they are equal sequences.

Constraints

* All values in input are integers.
* 1 \leq N \leq 2\times 10^5
* 1 \leq K \leq 10^9
* 1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 A_2 \cdots A_N


Output

Print the number of subsequences that satisfy the condition.

Examples

Input

5 4
1 4 2 3 5


Output

4


Input

8 4
4 2 4 2 4 2 4 2


Output

7


Input

10 7
14 15 92 65 35 89 79 32 38 46


Output

8

### Response

```cpp
#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int N=5000005;
ll n,m;
map<ll,ll>sq;
ll sum[N]={0};
ll a[N];
int main(){
	ll ans=0;
	cin>>n>>m;
	for(int i=1;i<=n;i++){
		cin>>a[i];
		sum[i]=sum[i-1]+a[i];
		
	}
	for(int i=1;i<=n;i++){
		sum[i]=(sum[i]-i%m+m)%m;
		
	}
	ll mn=min(m-1,n);
	for(int i=0;i<=mn;i++){
		ans+=sq[sum[i]];
		sq[sum[i]]++;
	}
	for(int i=mn+1;i<=n;i++)
    {
        sq[sum[i-m]]--;
        ans+=sq[sum[i]];
        sq[sum[i]]++;
    }	
	cout<<ans<<endl;
	return 0;
} 
```