#include<bits/stdc++.h>
using namespace std;
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	long long n,c=0,k,i,a,ans=0;
	unordered_map<long long,long long>m;
	cin>>n>>k;
	m[0]=1;
	vector<int>x(n+1);
	for(i=1;i<=n;i++)
	{
		if(i>=k)m[x[i-k]]--;
		cin>>a;
		c=(c+a)%k;
		x[i]=(c-i%k+k)%k;
		ans+=m[x[i]];
		m[x[i]]++;
	}
	cout<<ans<<'\n';
}

### 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;
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	long long n,c=0,k,i,a,ans=0;
	unordered_map<long long,long long>m;
	cin>>n>>k;
	m[0]=1;
	vector<int>x(n+1);
	for(i=1;i<=n;i++)
	{
		if(i>=k)m[x[i-k]]--;
		cin>>a;
		c=(c+a)%k;
		x[i]=(c-i%k+k)%k;
		ans+=m[x[i]];
		m[x[i]]++;
	}
	cout<<ans<<'\n';
}

```