#include<iostream>
#include<map>

int A[202020];
long long sum[202020];

int main(){
  int N,K;
  std::cin>>N>>K;
  for(int i=0;i<N;i++){
    std::cin>>A[i];
    sum[i+1]=sum[i]+A[i];
  }
  for(int i=1;i<=N;i++){
    sum[i]=sum[i]-i+K;
    (sum[i]%=K);
  }
  std::map<long long,int> mp;
  mp[sum[0]]++;
  long long ans=0;
  for(int i=1;i<=N;i++){
    if(i>=K) mp[sum[i-K]]--;
    ans+=mp[sum[i]];
    mp[sum[i]]++;
  }
  std::cout<<ans<<std::endl;
  return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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>
#include<map>

int A[202020];
long long sum[202020];

int main(){
  int N,K;
  std::cin>>N>>K;
  for(int i=0;i<N;i++){
    std::cin>>A[i];
    sum[i+1]=sum[i]+A[i];
  }
  for(int i=1;i<=N;i++){
    sum[i]=sum[i]-i+K;
    (sum[i]%=K);
  }
  std::map<long long,int> mp;
  mp[sum[0]]++;
  long long ans=0;
  for(int i=1;i<=N;i++){
    if(i>=K) mp[sum[i-K]]--;
    ans+=mp[sum[i]];
    mp[sum[i]]++;
  }
  std::cout<<ans<<std::endl;
  return 0;
}
```