#include <bits/stdc++.h>
#define Int int64_t

using namespace std;

int main() {
	Int N, K;
	cin >> N >> K;
	vector<Int> a(N + 1, 0);
	vector<Int> S(N + 1, 0);
	for (int i = 1; i <= N; ++i) {
		cin >> a[i];
		S[i] = S[i - 1] + a[i];
	}

	map<Int, Int> mp;
	Int ans = 0;
	for (int i = 0; i <= N; ++i) {
		if (i - K >= 0) { mp[ (S[i - K] - i + K) % K ] -= 1; }
		
		Int idx = (S[i] - i + K) % K;
		ans += mp[idx];
		mp[idx] += 1;
	}
	cout << ans << endl;

	return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>
#define Int int64_t

using namespace std;

int main() {
	Int N, K;
	cin >> N >> K;
	vector<Int> a(N + 1, 0);
	vector<Int> S(N + 1, 0);
	for (int i = 1; i <= N; ++i) {
		cin >> a[i];
		S[i] = S[i - 1] + a[i];
	}

	map<Int, Int> mp;
	Int ans = 0;
	for (int i = 0; i <= N; ++i) {
		if (i - K >= 0) { mp[ (S[i - K] - i + K) % K ] -= 1; }
		
		Int idx = (S[i] - i + K) % K;
		ans += mp[idx];
		mp[idx] += 1;
	}
	cout << ans << endl;

	return 0;
}

```