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

int N,K;
vector<int> A;
vector<int> c;

signed main()
{
  cin >> N >> K;
  A.resize(N);
  c.resize(N+1);

  for(int i=0; i<N; i++) cin >> A[i];
  for(int i=0; i<N; i++) c[i+1] = (c[i] + A[i] - 1) % K;

  int count=0;
  unordered_map<int, int> m;
  m[0]=1;
  for(int i=1; i<=N; i++)
  {
    if( i - K >= 0 ) m[c[i-K]]--;
    count += m[c[i]];
    m[c[i]]++;
  }
  cout << count << endl;
}

### Prompt

Generate 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;
#define int long long

int N,K;
vector<int> A;
vector<int> c;

signed main()
{
  cin >> N >> K;
  A.resize(N);
  c.resize(N+1);

  for(int i=0; i<N; i++) cin >> A[i];
  for(int i=0; i<N; i++) c[i+1] = (c[i] + A[i] - 1) % K;

  int count=0;
  unordered_map<int, int> m;
  m[0]=1;
  for(int i=1; i<=N; i++)
  {
    if( i - K >= 0 ) m[c[i-K]]--;
    count += m[c[i]];
    m[c[i]]++;
  }
  cout << count << endl;
}

```