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

int32_t main(){
	// freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
	int n,k;
	cin >> n >> k;
	int a[n+1];
	map <int,int> m;
	a[0]=0;
	for(int i=1;i<=n;i++){
		cin >> a[i];
		a[i]=(a[i]-1+a[i-1])%k;
	}
	int sum=0;
	m[0]++;
	for(int i=1;i<=min(n,k-1);i++){
		sum+=m[a[i]];
		m[a[i]]++;
	}
	for(int i=k;i<=n;i++){
		m[a[i-k]]--;
		sum+=m[a[i]];
		m[a[i]]++;
	}
	cout << sum << 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 <bits/stdc++.h>
#define int long long
using namespace std;

int32_t main(){
	// freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
	int n,k;
	cin >> n >> k;
	int a[n+1];
	map <int,int> m;
	a[0]=0;
	for(int i=1;i<=n;i++){
		cin >> a[i];
		a[i]=(a[i]-1+a[i-1])%k;
	}
	int sum=0;
	m[0]++;
	for(int i=1;i<=min(n,k-1);i++){
		sum+=m[a[i]];
		m[a[i]]++;
	}
	for(int i=k;i<=n;i++){
		m[a[i-k]]--;
		sum+=m[a[i]];
		m[a[i]]++;
	}
	cout << sum << endl;
}

```