#include <vector>
#include <iostream>
#include <map>
using namespace std;

int main(){
  int N, K;
  cin >> N >> K;
  vector<long long> A(N+1);
  for(int i = 1; i <= N; ++i)
    cin >> A[i], A[i] +=  K-1+A[i-1], A[i] %= K;
  
  map<int,int> C;
  long long ans = 0;
  ++C[0];
  for(int i = 1; i <= N; ++i){
    A[i] %= K;
    if(i >= K) --C[A[i-K]];
    // cerr << i << " " << C[A[i]] << endl;
    ans += C[A[i]];
    ++C[A[i]];
  }
  cout << ans << endl;
}

### Prompt

Your task is to create 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 <vector>
#include <iostream>
#include <map>
using namespace std;

int main(){
  int N, K;
  cin >> N >> K;
  vector<long long> A(N+1);
  for(int i = 1; i <= N; ++i)
    cin >> A[i], A[i] +=  K-1+A[i-1], A[i] %= K;
  
  map<int,int> C;
  long long ans = 0;
  ++C[0];
  for(int i = 1; i <= N; ++i){
    A[i] %= K;
    if(i >= K) --C[A[i-K]];
    // cerr << i << " " << C[A[i]] << endl;
    ans += C[A[i]];
    ++C[A[i]];
  }
  cout << ans << endl;
}

```