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

const int64_t N = int64_t(1e9);

int main() {
	int n, k;
	cin >> n >> k;
	map<int, int> cnt;
	int64_t ans = 0;
	int s = 0;
	cnt[0]++;
	queue<int> q;
	q.push(0);
	for (int i = 0; i < n; i++) {
		int x;
		cin >> x;
		s = (s + x - 1) % k;
		q.push(s);
		if (q.size() > k) {
			cnt[q.front()]--;
			q.pop();
		}
		ans += cnt[s];
		cnt[s]++;
	}
	cout << ans << endl;
	return 0;
}
### Prompt

Create a solution in CPP for 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;

const int64_t N = int64_t(1e9);

int main() {
	int n, k;
	cin >> n >> k;
	map<int, int> cnt;
	int64_t ans = 0;
	int s = 0;
	cnt[0]++;
	queue<int> q;
	q.push(0);
	for (int i = 0; i < n; i++) {
		int x;
		cin >> x;
		s = (s + x - 1) % k;
		q.push(s);
		if (q.size() > k) {
			cnt[q.front()]--;
			q.pop();
		}
		ans += cnt[s];
		cnt[s]++;
	}
	cout << ans << endl;
	return 0;
}
```