#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main() {
  int N, K;
  cin >> N >> K;
  vector<ll> A(N), B(N + 1);
  for (int i = 0; i < N; i++) cin >> A[i];

  ll ans = 0;
  for (int i = 0; i < N; i++) {
    B[i + 1] = B[i] + A[i];
  }

  for (int i = 1; i <= N; i++) {
    B[i] = (B[i] - i) % K;
  }

  map<ll, ll> m;
  for (int i = 0; i <= N; i++) {
    if (i - K >= 0) m[B[i - K]]--;
    ans += m[B[i]];
    m[B[i]]++;
  }
  cout << ans << endl;
}
### 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 <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main() {
  int N, K;
  cin >> N >> K;
  vector<ll> A(N), B(N + 1);
  for (int i = 0; i < N; i++) cin >> A[i];

  ll ans = 0;
  for (int i = 0; i < N; i++) {
    B[i + 1] = B[i] + A[i];
  }

  for (int i = 1; i <= N; i++) {
    B[i] = (B[i] - i) % K;
  }

  map<ll, ll> m;
  for (int i = 0; i <= N; i++) {
    if (i - K >= 0) m[B[i - K]]--;
    ans += m[B[i]];
    m[B[i]]++;
  }
  cout << ans << endl;
}
```