#include<iostream>
#define ll long long int
#include<bits/stdc++.h>

using namespace std;

int main()
{
ll n,k,cursum=0,res=0;
  cin>>n>>k;
  vector<ll> arr(n);
  vector<ll> sum(n+1);
  sum[0]=0;
  for(int i=0;i<n;i++)
  {
    cin>>arr[i];
    sum[i+1]=sum[i]+arr[i];
  }
  queue<ll> q;
  map<ll,ll> count;
  for(int i=0;i<=n;i++)
  {
    cursum=(sum[i]-i)%k;
    q.push(cursum);
    res+=count[cursum];
    count[cursum]++;
    if(q.size()>=k)
    {
      count[q.front()]--;
    	q.pop();
  	}
  }
  cout<<res<<endl;
  return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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<iostream>
#define ll long long int
#include<bits/stdc++.h>

using namespace std;

int main()
{
ll n,k,cursum=0,res=0;
  cin>>n>>k;
  vector<ll> arr(n);
  vector<ll> sum(n+1);
  sum[0]=0;
  for(int i=0;i<n;i++)
  {
    cin>>arr[i];
    sum[i+1]=sum[i]+arr[i];
  }
  queue<ll> q;
  map<ll,ll> count;
  for(int i=0;i<=n;i++)
  {
    cursum=(sum[i]-i)%k;
    q.push(cursum);
    res+=count[cursum];
    count[cursum]++;
    if(q.size()>=k)
    {
      count[q.front()]--;
    	q.pop();
  	}
  }
  cout<<res<<endl;
  return 0;
}
```