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

int n,k,ans=0;
int a[200005],pre[200005];

map<int,int> m;

signed main()
{
	cin>>n>>k;
	if (k==1)  return cout<<0<<endl,0;
	for (int i=1;i<=n;i++)  cin>>a[i];
	for (int i=1;i<=n;i++)  a[i]--;
	for (int i=1;i<=n;i++)  pre[i]=(pre[i-1]+a[i])%k;

	m[0]=1;
	for (int i=1;i<=n;i++)
	{
		ans+=m[pre[i]];
		m[pre[i]]++;
		if (i>=k-1)  m[pre[i-k+1]]--;
	}
	cout<<ans<<endl;
	
	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>
#define int long long
using namespace std;

int n,k,ans=0;
int a[200005],pre[200005];

map<int,int> m;

signed main()
{
	cin>>n>>k;
	if (k==1)  return cout<<0<<endl,0;
	for (int i=1;i<=n;i++)  cin>>a[i];
	for (int i=1;i<=n;i++)  a[i]--;
	for (int i=1;i<=n;i++)  pre[i]=(pre[i-1]+a[i])%k;

	m[0]=1;
	for (int i=1;i<=n;i++)
	{
		ans+=m[pre[i]];
		m[pre[i]]++;
		if (i>=k-1)  m[pre[i-k+1]]--;
	}
	cout<<ans<<endl;
	
	return 0;
}
```