#include <bits/stdc++.h>
#define X first
#define Y second
typedef long long ll;
using namespace std;

const int MOD = 1e9 + 7;
const ll INF = 1e18;

int n, k;
map<int, int> m;
int zbr[200002];

int main () {

	cin >> n >> k;
	m[0] ++;
	ll sol = 0;
	for (int i = 1; i <= n; i++) {
		if (i-k >= 0) m[zbr[i-k]] --;
		cin >> zbr[i];
		zbr[i] --;
		zbr[i] += zbr[i-1];
		zbr[i] %= k;
		sol += m[zbr[i]];
		m[zbr[i]] ++;
	}
	
	cout << sol;

	return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 X first
#define Y second
typedef long long ll;
using namespace std;

const int MOD = 1e9 + 7;
const ll INF = 1e18;

int n, k;
map<int, int> m;
int zbr[200002];

int main () {

	cin >> n >> k;
	m[0] ++;
	ll sol = 0;
	for (int i = 1; i <= n; i++) {
		if (i-k >= 0) m[zbr[i-k]] --;
		cin >> zbr[i];
		zbr[i] --;
		zbr[i] += zbr[i-1];
		zbr[i] %= k;
		sol += m[zbr[i]];
		m[zbr[i]] ++;
	}
	
	cout << sol;

	return 0;
}
```