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

signed main(){
	int N, K, A, S = 0, i, ans = 0;
	scanf("%lld%lld", &N, &K);
	map<int, int> mp;
	queue<int> q;
	mp[S]++;
	q.push(S);
	for(i = 0; i < N; i++){
		if(q.size() >= K){
			mp[q.front()]--;
			q.pop();
		}
		scanf("%lld", &A);
		S = (S + A - 1) % K;
//		printf("S = %lld\n", S);
		ans += mp[S];
//		printf("ans = %lld\n", ans);
		mp[S]++;
		q.push(S);
	}
	printf("%lld\n", ans);
	return 0;
}
### Prompt

Please formulate 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>
using namespace std;
#define int long long

signed main(){
	int N, K, A, S = 0, i, ans = 0;
	scanf("%lld%lld", &N, &K);
	map<int, int> mp;
	queue<int> q;
	mp[S]++;
	q.push(S);
	for(i = 0; i < N; i++){
		if(q.size() >= K){
			mp[q.front()]--;
			q.pop();
		}
		scanf("%lld", &A);
		S = (S + A - 1) % K;
//		printf("S = %lld\n", S);
		ans += mp[S];
//		printf("ans = %lld\n", ans);
		mp[S]++;
		q.push(S);
	}
	printf("%lld\n", ans);
	return 0;
}
```