#include <bits/stdc++.h>

using namespace std;

int main() {
  int n; long long k;
  cin >> n >> k;
  vector <long long> p(n + 1, 0);
  long long cur = 0;
  map <long long, long long> cnt;
  cnt[0] = 1;
  long long ans = 0;
  for(int i = 0; i < n; i++) {
    long long x; cin >> x;
    x--;
    cur = (cur + x) % k;
    p[i + 1] = cur;
    if(i >= k - 1) cnt[p[i - k + 1]]--;
    if(cnt.count(cur)) {
      ans += cnt[cur];
      cnt[cur] += 1;
    }
    else {
      cnt[cur] = 1;
    }
  }
  cout << ans << '\n';
}
### Prompt

Create a solution in CPP for 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() {
  int n; long long k;
  cin >> n >> k;
  vector <long long> p(n + 1, 0);
  long long cur = 0;
  map <long long, long long> cnt;
  cnt[0] = 1;
  long long ans = 0;
  for(int i = 0; i < n; i++) {
    long long x; cin >> x;
    x--;
    cur = (cur + x) % k;
    p[i + 1] = cur;
    if(i >= k - 1) cnt[p[i - k + 1]]--;
    if(cnt.count(cur)) {
      ans += cnt[cur];
      cnt[cur] += 1;
    }
    else {
      cnt[cur] = 1;
    }
  }
  cout << ans << '\n';
}
```