#include <bits/stdc++.h>

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]--;
  vector<int> s(n + 1, 0);
  for (int i = 0; i < n; i++) s[i + 1] = (s[i] + a[i]) % k;
  map<int, int> mp;
  long long ans = 0;
  queue<int> q;
  for (int i = 0; i < n + 1; i++) {
    ans += mp[s[i]];
    mp[s[i]]++;
    q.push(s[i]);
    if (q.size() == k) {
      mp[q.front()]--;
      q.pop();
    }
  }
  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() {
  int n, k;
  cin >> n >> k;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i], a[i]--;
  vector<int> s(n + 1, 0);
  for (int i = 0; i < n; i++) s[i + 1] = (s[i] + a[i]) % k;
  map<int, int> mp;
  long long ans = 0;
  queue<int> q;
  for (int i = 0; i < n + 1; i++) {
    ans += mp[s[i]];
    mp[s[i]]++;
    q.push(s[i]);
    if (q.size() == k) {
      mp[q.front()]--;
      q.pop();
    }
  }
  cout << ans << endl;

  return 0;
}
```