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

int main() {
	static long long N, K, A[200000], SUM[200010] = {}, COUNT = 0, ANS = 0;
	cin >> N >> K;
	for (int i = 0; i < N; i++) {
		cin >> A[i];
		A[i] %= K;
		A[i] = (A[i] - 1 + K) % K;
		SUM[i + 1] = (SUM[i] + A[i]) % K;
	}
	map<long long, long long> mp;
	if (K != 1) mp[0]++;
	for (int i = 1; i <= N; i++) {
		ANS += mp[SUM[i]];
		mp[SUM[i]]++;
		if (i >= K - 1) mp[SUM[i - K + 1]]--;
	}
	cout << ANS << endl;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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;

int main() {
	static long long N, K, A[200000], SUM[200010] = {}, COUNT = 0, ANS = 0;
	cin >> N >> K;
	for (int i = 0; i < N; i++) {
		cin >> A[i];
		A[i] %= K;
		A[i] = (A[i] - 1 + K) % K;
		SUM[i + 1] = (SUM[i] + A[i]) % K;
	}
	map<long long, long long> mp;
	if (K != 1) mp[0]++;
	for (int i = 1; i <= N; i++) {
		ANS += mp[SUM[i]];
		mp[SUM[i]]++;
		if (i >= K - 1) mp[SUM[i - K + 1]]--;
	}
	cout << ANS << endl;
}
```