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

```