#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
map<int,int> mmp;
int A[222222];
int main() {
	int N,K;
	scanf("%d%d",&N,&K);
	for(int i=1; i<=N; ++i) scanf("%d",A+i);
	for(int i=1; i<=N; ++i) A[i]=(A[i-1]+A[i]-1)%K;
	LL ans=0;
	mmp[0]++;
	for(int l=0,r=1; r<=N; ++r) {
		if(r-l==K) mmp[A[l++]]--;
		ans+=mmp[A[r]];
		mmp[A[r]]++;
	}
	printf("%lld",ans);
	return 0;
}
### Prompt

Create a solution in Cpp for 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;
typedef long long LL;
map<int,int> mmp;
int A[222222];
int main() {
	int N,K;
	scanf("%d%d",&N,&K);
	for(int i=1; i<=N; ++i) scanf("%d",A+i);
	for(int i=1; i<=N; ++i) A[i]=(A[i-1]+A[i]-1)%K;
	LL ans=0;
	mmp[0]++;
	for(int l=0,r=1; r<=N; ++r) {
		if(r-l==K) mmp[A[l++]]--;
		ans+=mmp[A[r]];
		mmp[A[r]]++;
	}
	printf("%lld",ans);
	return 0;
}
```