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

const int N = (int) 2e5 + 5;

int n, k;
long long a[N], s[N];
map <long long, long long> remain;

int main() {
	ios_base :: sync_with_stdio(false); cin.tie(NULL);
	cin >> n >> k;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		s[i] = s[i - 1] + a[i];
	}
	remain[s[0] - 0]++;
	long long ans = 0;
	for (int i = 1; i <= n; i++) {
		if (i - k >= 0) remain[(s[i - k] - (i - k)) % k]--;
		ans += remain[(s[i] - i) % k]++;
	}
	cout << ans << "\n";
	return 0;
}
### Prompt

Please create a solution in cpp 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 N = (int) 2e5 + 5;

int n, k;
long long a[N], s[N];
map <long long, long long> remain;

int main() {
	ios_base :: sync_with_stdio(false); cin.tie(NULL);
	cin >> n >> k;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
		s[i] = s[i - 1] + a[i];
	}
	remain[s[0] - 0]++;
	long long ans = 0;
	for (int i = 1; i <= n; i++) {
		if (i - k >= 0) remain[(s[i - k] - (i - k)) % k]--;
		ans += remain[(s[i] - i) % k]++;
	}
	cout << ans << "\n";
	return 0;
}
```