#include<bits/stdc++.h>
using namespace std;
int cnt[200003],n,k;
long long ans;
map<int,int>mp;
int main(){
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		int a;
		cin>>a;
		cnt[i]=(cnt[i-1]+a-1)%k;
	}
	mp[0]=1;
	for(int i=1;i<=n;i++)
	{
		if(i>=k)mp[cnt[i-k]]--;
		ans+=mp[cnt[i]],mp[cnt[i]]++;
	}
	cout<<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;
int cnt[200003],n,k;
long long ans;
map<int,int>mp;
int main(){
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		int a;
		cin>>a;
		cnt[i]=(cnt[i-1]+a-1)%k;
	}
	mp[0]=1;
	for(int i=1;i<=n;i++)
	{
		if(i>=k)mp[cnt[i-k]]--;
		ans+=mp[cnt[i]],mp[cnt[i]]++;
	}
	cout<<ans;
}
```