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


signed main(){
  int n,k;cin>>n>>k;
  vector<int> v(n);
  for(int i=0;i<n;i++)cin>>v[i];
  for(int i=0;i<n;i++)v[i]=(v[i]+k-1)%k;
  vector<int> w(n+1,0);
  for(int i=0;i<n;i++)w[i+1]=(v[i]+w[i])%k;
  map<int,int> m;
  int ans=0;
  for(int i=0;i<=n;i++){
    if(i>=k)m[w[i-k]]--;
    ans+=m[w[i]];
    m[w[i]]++;
  }
  cout<<ans<<endl;
}

### Prompt

Create a solution in cpp for 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 int long long


signed main(){
  int n,k;cin>>n>>k;
  vector<int> v(n);
  for(int i=0;i<n;i++)cin>>v[i];
  for(int i=0;i<n;i++)v[i]=(v[i]+k-1)%k;
  vector<int> w(n+1,0);
  for(int i=0;i<n;i++)w[i+1]=(v[i]+w[i])%k;
  map<int,int> m;
  int ans=0;
  for(int i=0;i<=n;i++){
    if(i>=k)m[w[i-k]]--;
    ans+=m[w[i]];
    m[w[i]]++;
  }
  cout<<ans<<endl;
}

```