#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
/*
  sum of subarr % K == num of elements
  
*/
const int N = 2e5 + 10;
int n; ll k;
ll a[N], s[N];
map<ll, int> cnt;

int main() {
	cin >> n >> k; for (int i = 1; i <= n; ++i) {
		cin >> a[i]; a[i]--;
	}
	s[1] = a[1]%k; for (int i = 2; i <= n; ++i) s[i] = (s[i - 1] + a[i]) % k;
	ll ans = 0;// cnt[0] = 1;
	for (int i = 0; i <= n; ++i) {
		ans += cnt[s[i]];
		cnt[s[i]]++;
		if (i - k + 1 >= 0) cnt[s[i - k + 1]]--;
	}
	cout << ans << endl;
}
### Prompt

Generate 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;
typedef long long ll;
/*
  sum of subarr % K == num of elements
  
*/
const int N = 2e5 + 10;
int n; ll k;
ll a[N], s[N];
map<ll, int> cnt;

int main() {
	cin >> n >> k; for (int i = 1; i <= n; ++i) {
		cin >> a[i]; a[i]--;
	}
	s[1] = a[1]%k; for (int i = 2; i <= n; ++i) s[i] = (s[i - 1] + a[i]) % k;
	ll ans = 0;// cnt[0] = 1;
	for (int i = 0; i <= n; ++i) {
		ans += cnt[s[i]];
		cnt[s[i]]++;
		if (i - k + 1 >= 0) cnt[s[i - k + 1]]--;
	}
	cout << ans << endl;
}
```