#include<iostream>
#include<map>
using namespace std;
int N,K;
map<int,int>M;
long pre[2<<17];
int main()
{
	cin>>N>>K;
	long ans=0;
	M[0]=1;
	pre[0]=0;
	long now=0;
	for(int i=0;i<N;i++)
	{
		long A;cin>>A;
		now=(now+A-1)%K;
		pre[i+1]=now;
		if(K<=i+1)M[pre[i+1-K]]--;
		ans+=M[now]++;
	}
	cout<<ans<<endl;
}

### Prompt

Your challenge is to write 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<iostream>
#include<map>
using namespace std;
int N,K;
map<int,int>M;
long pre[2<<17];
int main()
{
	cin>>N>>K;
	long ans=0;
	M[0]=1;
	pre[0]=0;
	long now=0;
	for(int i=0;i<N;i++)
	{
		long A;cin>>A;
		now=(now+A-1)%K;
		pre[i+1]=now;
		if(K<=i+1)M[pre[i+1-K]]--;
		ans+=M[now]++;
	}
	cout<<ans<<endl;
}

```