#include<bits/stdc++.h>
using namespace std;
int main(){
  long long res = 0;
  long long n,k;cin>>n>>k;
  vector<long long> arr(n+1);
  for(int i=1;i<=n;++i){cin>>arr[i];}
  for(int i=1;i<=n;++i){arr[i]+=arr[i-1];}
  map<int,int> mp1;
  for(int i=0;i<=n;++i){
    int curr = (arr[i]-i)%k;
    if(i>=k){
      int lst =  (arr[i-k]-i+k)%k;
      mp1[lst]--;
    }
    res+=mp1[curr];
    mp1[curr]++;
  }
  cout<<res<<endl;
  return 0;
}

### Prompt

Please formulate 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;
int main(){
  long long res = 0;
  long long n,k;cin>>n>>k;
  vector<long long> arr(n+1);
  for(int i=1;i<=n;++i){cin>>arr[i];}
  for(int i=1;i<=n;++i){arr[i]+=arr[i-1];}
  map<int,int> mp1;
  for(int i=0;i<=n;++i){
    int curr = (arr[i]-i)%k;
    if(i>=k){
      int lst =  (arr[i-k]-i+k)%k;
      mp1[lst]--;
    }
    res+=mp1[curr];
    mp1[curr]++;
  }
  cout<<res<<endl;
  return 0;
}

```