#include <bits/stdc++.h>
#define int long long

using namespace std;

int n=0,k=0;
int a[200001];
int s[200001];
map<int, int> Map;

signed main()
{
	cin >> n >> k;
	for (int i=1; i<=n; i++)
	{
		cin >> a[i];
	}
	s[0] = 0;
	for (int i=1; i<=n; i++)
	{
		s[i] = s[i-1]+a[i];
	}
	Map[0]++;
	int res=0;
	for (int i=1; i<=n; i++)
	{
		if (i-k>=0)	
		{
			Map[(s[i-k]-(i-k))%k]--;		
		}	
		res+=Map[(s[i]-i)%k];
		Map[(s[i]-i)%k]++;	
	}		
	cout << res;
	return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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>
#define int long long

using namespace std;

int n=0,k=0;
int a[200001];
int s[200001];
map<int, int> Map;

signed main()
{
	cin >> n >> k;
	for (int i=1; i<=n; i++)
	{
		cin >> a[i];
	}
	s[0] = 0;
	for (int i=1; i<=n; i++)
	{
		s[i] = s[i-1]+a[i];
	}
	Map[0]++;
	int res=0;
	for (int i=1; i<=n; i++)
	{
		if (i-k>=0)	
		{
			Map[(s[i-k]-(i-k))%k]--;		
		}	
		res+=Map[(s[i]-i)%k];
		Map[(s[i]-i)%k]++;	
	}		
	cout << res;
	return 0;
}

```