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

int main() {
  int N,K;
  int64_t Z=0;
  cin>>N>>K;
  vector<int> p(N);
  for(int i=0;i<N;i++){
    cin>>p[i];
    p[i]--;
  }
  vector<int> q(N+1);
  map<int,int> m;
  m[0]=1;
  for(int i=0;i<N;i++){
    int j=i+1-K;
    if(j>=0){
      m[q[j]]--;
    }
    q[i+1]=(q[i]+p[i])%K;
    if(m.count(q[i+1])){
      m[q[i+1]]++;
    }
    else{
      m[q[i+1]]=1;
    }
    Z+=m[q[i+1]]-1;
  }
  cout<<Z<<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;

int main() {
  int N,K;
  int64_t Z=0;
  cin>>N>>K;
  vector<int> p(N);
  for(int i=0;i<N;i++){
    cin>>p[i];
    p[i]--;
  }
  vector<int> q(N+1);
  map<int,int> m;
  m[0]=1;
  for(int i=0;i<N;i++){
    int j=i+1-K;
    if(j>=0){
      m[q[j]]--;
    }
    q[i+1]=(q[i]+p[i])%K;
    if(m.count(q[i+1])){
      m[q[i+1]]++;
    }
    else{
      m[q[i+1]]=1;
    }
    Z+=m[q[i+1]]-1;
  }
  cout<<Z<<endl;
}
```