#include <iostream>
#include <map>

using namespace std;
using ll = long long;

#define rep(i,n) for(int i=0;i<(n);++i)
int main() {
  int N, K; cin >> N >> K;

  ll A[N], sum[N+1];
  sum[0] = 0;
  rep(i, N) {
    cin >> A[i];
    --A[i];
    sum[i+1] = sum[i] + A[i];
    sum[i+1] %= K;
  }
  ll ans = 0;
  map<ll, int> m;
  rep(i, min(N+1, K)) {
    ++m[sum[i]];
  }
  rep(l, N) {
    --m[sum[l]];
    ans += m[sum[l]];
    if (l+K < N+1)
      ++m[sum[l+K]];
  }
  cout << ans << endl;

  return 0;
}

### 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 <iostream>
#include <map>

using namespace std;
using ll = long long;

#define rep(i,n) for(int i=0;i<(n);++i)
int main() {
  int N, K; cin >> N >> K;

  ll A[N], sum[N+1];
  sum[0] = 0;
  rep(i, N) {
    cin >> A[i];
    --A[i];
    sum[i+1] = sum[i] + A[i];
    sum[i+1] %= K;
  }
  ll ans = 0;
  map<ll, int> m;
  rep(i, min(N+1, K)) {
    ++m[sum[i]];
  }
  rep(l, N) {
    --m[sum[l]];
    ans += m[sum[l]];
    if (l+K < N+1)
      ++m[sum[l+K]];
  }
  cout << ans << endl;

  return 0;
}

```