#include<bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < n; ++i )
using namespace std;
using ll = long long;

int main() {
  ll n,k; cin >> n >> k;
  vector<int> a(n);
  rep(i,n) cin >> a[i];

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

  ll ans = 0;
  map<int,int> mp;
  int l = 0;
  rep(r,n+1){
    if(r-l+1>k){
      mp[m[l]]--;
      ++l;
    }
    ans += mp[m[r]];
    mp[m[r]]++;
  }
  cout << ans << endl;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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>
#define rep(i,n) for(int i = 0; i < n; ++i )
using namespace std;
using ll = long long;

int main() {
  ll n,k; cin >> n >> k;
  vector<int> a(n);
  rep(i,n) cin >> a[i];

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

  ll ans = 0;
  map<int,int> mp;
  int l = 0;
  rep(r,n+1){
    if(r-l+1>k){
      mp[m[l]]--;
      ++l;
    }
    ans += mp[m[r]];
    mp[m[r]]++;
  }
  cout << ans << endl;
}

```