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

typedef long long ll;
typedef pair<int, int> ii;

const int N = 2e5 + 5;
int n, k, t, sum;
ll res;
int temp[N];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  cin >> n >> k;
  unordered_map<int, int> ma;
  ma[0] = 1;
  for (int i = 1; i <= n; ++i) {
    if (i >= k) {
      --ma[temp[i - k]];
    }
    cin >> t;
    sum = (sum + t - 1) % k;
    temp[i] = sum;
    if (ma.count(sum))
      res += ma[sum];
    ++ma[sum];
  }
  cout << res << endl;
  
  return 0;
}

### Prompt

Please create a solution in Cpp 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;

typedef long long ll;
typedef pair<int, int> ii;

const int N = 2e5 + 5;
int n, k, t, sum;
ll res;
int temp[N];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  cin >> n >> k;
  unordered_map<int, int> ma;
  ma[0] = 1;
  for (int i = 1; i <= n; ++i) {
    if (i >= k) {
      --ma[temp[i - k]];
    }
    cin >> t;
    sum = (sum + t - 1) % k;
    temp[i] = sum;
    if (ma.count(sum))
      res += ma[sum];
    ++ma[sum];
  }
  cout << res << endl;
  
  return 0;
}

```