#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL_DEBUG
  #include "LOCAL_DEBUG.hpp"
#endif
#define int long long

signed main(){

  int n, k; cin >> n >> k;
  vector<int> a(n);
  for(int i = 0; i < n; i++) cin >> a[i];

  vector<int> imos(n+1, 0);
  for(int i = 0; i < n; i++){
    imos[i+1] = (imos[i] + a[i] - 1) % k;
  }

  int ans = 0;
  map<int, int> mp;
  for(int i = 0; i <= n; i++){
    if(i - k >= 0) mp[imos[i - k]]--;
    ans += mp[imos[i]];
    mp[imos[i]]++;
  }
  cout << ans << endl;

  return 0;
}

### Prompt

Please create a solution in CPP 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;
#ifdef LOCAL_DEBUG
  #include "LOCAL_DEBUG.hpp"
#endif
#define int long long

signed main(){

  int n, k; cin >> n >> k;
  vector<int> a(n);
  for(int i = 0; i < n; i++) cin >> a[i];

  vector<int> imos(n+1, 0);
  for(int i = 0; i < n; i++){
    imos[i+1] = (imos[i] + a[i] - 1) % k;
  }

  int ans = 0;
  map<int, int> mp;
  for(int i = 0; i <= n; i++){
    if(i - k >= 0) mp[imos[i - k]]--;
    ans += mp[imos[i]];
    mp[imos[i]]++;
  }
  cout << ans << endl;

  return 0;
}

```