#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int main(){
  ll n,k;cin >> n >> k;
  vector<ll> a(n),sum(n+1);
  for(int i=0;i<n;i++){
    cin >> a[i];
    sum[i+1]=sum[i]+a[i];
  }
  for(ll i=0;i<n+1;i++){
    sum[i]=(sum[i]+n*k-i)%k;
  }
  map<int,int> mp;
  ll ans=0;
  for(int i=0;i<=n;i++){
    ans+=mp[sum[i]];
    mp[sum[i]]++;
    if(i>=k-1){
      mp[sum[i-(k-1)]]--;
    }
  }
  cout << ans << endl;
}
### Prompt

Your task is to create 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;
typedef long long ll;
int main(){
  ll n,k;cin >> n >> k;
  vector<ll> a(n),sum(n+1);
  for(int i=0;i<n;i++){
    cin >> a[i];
    sum[i+1]=sum[i]+a[i];
  }
  for(ll i=0;i<n+1;i++){
    sum[i]=(sum[i]+n*k-i)%k;
  }
  map<int,int> mp;
  ll ans=0;
  for(int i=0;i<=n;i++){
    ans+=mp[sum[i]];
    mp[sum[i]]++;
    if(i>=k-1){
      mp[sum[i-(k-1)]]--;
    }
  }
  cout << ans << endl;
}
```