#include <bits/stdc++.h>

using namespace std;

int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);

  int N, K; cin>>N>>K;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
	A[i] -= 1;
    if (i > 0)
      A[i] += A[i-1];
    A[i] %= K;
  }

  unordered_map<int, size_t> cands;
  for (int i = 0; i < min(K-1, N); i++)
    cands[A[i]]++;
  long ans = cands[0];
  for (int i = 0; i < N-1; i++) {
	if (i+K-1 < N)
	  cands[A[i+K-1]]++;
    ans += --cands[A[i]];
  }

  cout << ans << endl;

  return 0;
}

### 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;

int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);

  int N, K; cin>>N>>K;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
	A[i] -= 1;
    if (i > 0)
      A[i] += A[i-1];
    A[i] %= K;
  }

  unordered_map<int, size_t> cands;
  for (int i = 0; i < min(K-1, N); i++)
    cands[A[i]]++;
  long ans = cands[0];
  for (int i = 0; i < N-1; i++) {
	if (i+K-1 < N)
	  cands[A[i+K-1]]++;
    ans += --cands[A[i]];
  }

  cout << ans << endl;

  return 0;
}

```