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

typedef long long ll;
const int N = 2e5 + 100;

int n, k, a, ps[N];
ll ans;
unordered_map<int, int> cnt;

int main() {
	cin >> n >> k;
	cnt[0]++;
	int now = 0;
	int add = 0;
	for (int i = 1; i <= n; i++) {
		cin >> a;
		now = (now + a) % k;
		add = (add + 1) % k;
		ps[i] = now;
		if (i >= k)
			cnt[(ps[i - k] + k - add) % k]--;
		ans += cnt[(now - add + k) % k];
		cnt[(now - add + k) % k]++;
	}
	cout << ans;
}

### 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;

typedef long long ll;
const int N = 2e5 + 100;

int n, k, a, ps[N];
ll ans;
unordered_map<int, int> cnt;

int main() {
	cin >> n >> k;
	cnt[0]++;
	int now = 0;
	int add = 0;
	for (int i = 1; i <= n; i++) {
		cin >> a;
		now = (now + a) % k;
		add = (add + 1) % k;
		ps[i] = now;
		if (i >= k)
			cnt[(ps[i - k] + k - add) % k]--;
		ans += cnt[(now - add + k) % k];
		cnt[(now - add + k) % k]++;
	}
	cout << ans;
}

```