#include <map>
#include <vector>
#include <iostream>
using namespace std;
int main() {
	int N, K;
	cin >> N >> K;
	vector<int> A(N);
	for (int i = 0; i < N; ++i) {
		cin >> A[i];
		A[i] = (A[i] - 1) % K;
	}
	vector<int> S(N + 1);
	for (int i = 0; i < N; ++i) {
		S[i + 1] = (S[i] + A[i]) % K;
	}
	map<int, int> d;
	long long ans = 0;
	for (int i = 0; i <= N; ++i) {
		++d[S[i]];
		if (i >= K) --d[S[i - K]];
		ans += d[S[i]] - 1;
	}
	cout << ans << endl;
	return 0;
}
### Prompt

Your task is to create 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 <map>
#include <vector>
#include <iostream>
using namespace std;
int main() {
	int N, K;
	cin >> N >> K;
	vector<int> A(N);
	for (int i = 0; i < N; ++i) {
		cin >> A[i];
		A[i] = (A[i] - 1) % K;
	}
	vector<int> S(N + 1);
	for (int i = 0; i < N; ++i) {
		S[i + 1] = (S[i] + A[i]) % K;
	}
	map<int, int> d;
	long long ans = 0;
	for (int i = 0; i <= N; ++i) {
		++d[S[i]];
		if (i >= K) --d[S[i - K]];
		ans += d[S[i]] - 1;
	}
	cout << ans << endl;
	return 0;
}
```