#include<bits/stdc++.h>
using namespace std;
#define LL long long 
#define maxn 200005
LL s[maxn],ans;
map<int,int>mp;
int main(){
	int n,x,k;scanf("%d%d",&n,&k);
	mp[0]++;
	for(int i=1;i<=n;i++){
		scanf("%d",&x),s[i]=s[i-1]+x;
		if(i>=k)mp[(s[i-k]-i+k)%k]--;
		ans+=mp[(s[i]-i)%k]++;
	}
	printf("%lld",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 LL long long 
#define maxn 200005
LL s[maxn],ans;
map<int,int>mp;
int main(){
	int n,x,k;scanf("%d%d",&n,&k);
	mp[0]++;
	for(int i=1;i<=n;i++){
		scanf("%d",&x),s[i]=s[i-1]+x;
		if(i>=k)mp[(s[i-k]-i+k)%k]--;
		ans+=mp[(s[i]-i)%k]++;
	}
	printf("%lld",ans);
	return 0;
}
```