#include<bits/stdc++.h>
using namespace std;

typedef long long int ll;

int main()
{
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
    ll n,k;
    cin>>n>>k;
    ll prefix[n+1];
    prefix[0]=0;
    ll ans=0,pre=0,a;
    map<ll,ll> m;
    m[0]++;
    for(ll i=0;i<n;i++)
    {
     cin>>a;
     a--;
     pre+=a;
     pre=pre%k;
     prefix[i+1]=pre;
     if(i>=(k-1))
      m[prefix[i-(k-1)]]--;
      ans+=m[pre];
      m[pre]++;
    }
    cout<<ans<<"\n";
    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;

typedef long long int ll;

int main()
{
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
    ll n,k;
    cin>>n>>k;
    ll prefix[n+1];
    prefix[0]=0;
    ll ans=0,pre=0,a;
    map<ll,ll> m;
    m[0]++;
    for(ll i=0;i<n;i++)
    {
     cin>>a;
     a--;
     pre+=a;
     pre=pre%k;
     prefix[i+1]=pre;
     if(i>=(k-1))
      m[prefix[i-(k-1)]]--;
      ans+=m[pre];
      m[pre]++;
    }
    cout<<ans<<"\n";
    return 0;
}
```