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

int main(){
  int n,k; cin >> n >> k;
  vl a(n);
  rep(i,n){
    cin >> a[i];
    a[i]--;
  }
  vl s(n+1); rep(i,n) s[i+1] = (s[i] + a[i])%k;

  map<ll,int> C;
  queue<int> q;
  ll ans = 0LL;
  rep(i,n+1) {
    ans += C[s[i]];
    C[s[i]]++;
    q.push(s[i]);
    // 長さが k 以上隔てたペアはカウントしないようにする
    if(q.size() == k){
      C[q.front()]--;
      q.pop();
    }
  }

  cout << ans << endl;
}

### Prompt

In CPP, your task is to solve 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;
#define ll long long
#define rep(i,n) for (int i = 0; i < n; i++)
#define vl vector<ll>

int main(){
  int n,k; cin >> n >> k;
  vl a(n);
  rep(i,n){
    cin >> a[i];
    a[i]--;
  }
  vl s(n+1); rep(i,n) s[i+1] = (s[i] + a[i])%k;

  map<ll,int> C;
  queue<int> q;
  ll ans = 0LL;
  rep(i,n+1) {
    ans += C[s[i]];
    C[s[i]]++;
    q.push(s[i]);
    // 長さが k 以上隔てたペアはカウントしないようにする
    if(q.size() == k){
      C[q.front()]--;
      q.pop();
    }
  }

  cout << ans << endl;
}

```