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

const int inf = 1e9;

signed main () {
	int n, k;
	cin >> n >> k;
	vector < int > a(n + 1, 0), pref(n + 1, 0), p(n + 1, 0);
	for (int i = 1; i <= n; ++i) {
		cin >> a[i];
		pref[i] = (pref[i - 1] + a[i]) % k;
		p[i] = (pref[i] - i + ((inf / k) * k)) % k;
	}
	map < int, int > cnt;
	int64_t ans = 0;
	for (int i = 0; i <= n; ++i) {
		if (i >= k)
			--cnt[p[i - k]];
		ans += cnt[p[i]];
		++cnt[p[i]];
	}
	cout << ans << '\n';
}

### 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>
using namespace std;

const int inf = 1e9;

signed main () {
	int n, k;
	cin >> n >> k;
	vector < int > a(n + 1, 0), pref(n + 1, 0), p(n + 1, 0);
	for (int i = 1; i <= n; ++i) {
		cin >> a[i];
		pref[i] = (pref[i - 1] + a[i]) % k;
		p[i] = (pref[i] - i + ((inf / k) * k)) % k;
	}
	map < int, int > cnt;
	int64_t ans = 0;
	for (int i = 0; i <= n; ++i) {
		if (i >= k)
			--cnt[p[i - k]];
		ans += cnt[p[i]];
		++cnt[p[i]];
	}
	cout << ans << '\n';
}

```