#include<bits/stdc++.h>
using namespace std;

const int maxn=2e5+7;
int a[maxn],s[maxn],n,k;
map<int,int> m;
long long ans;

int main()
{
	scanf("%d %d",&n,&k);
	for(int i=1;i<=n;++i) {
		scanf("%d",&a[i]);
		s[i]=(s[i-1]+a[i])%k;
	}
	for(int i=1;i<=n;++i) s[i]=((s[i]-i)%k+k)%k;
	for(int i=0;i<=n;++i) {
		if(i-k>=0) m[s[i-k]]--;
		ans+=m[s[i]];
		m[s[i]]++;
	}
	printf("%lld",ans);
}
### Prompt

In CPP, your task is to solve 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>
using namespace std;

const int maxn=2e5+7;
int a[maxn],s[maxn],n,k;
map<int,int> m;
long long ans;

int main()
{
	scanf("%d %d",&n,&k);
	for(int i=1;i<=n;++i) {
		scanf("%d",&a[i]);
		s[i]=(s[i-1]+a[i])%k;
	}
	for(int i=1;i<=n;++i) s[i]=((s[i]-i)%k+k)%k;
	for(int i=0;i<=n;++i) {
		if(i-k>=0) m[s[i-k]]--;
		ans+=m[s[i]];
		m[s[i]]++;
	}
	printf("%lld",ans);
}
```