#include "bits/stdc++.h"

using namespace std;
using ll = long long;
#define REP(i, n) for (int i = 0; i < n; ++i)
#define ALL(v) v.begin(), v.end()

int main() {
  int n, k;
  cin >> n >> k;
  vector<int> v(n);
  REP(i, n) cin >> v[i];
  vector<ll> a(n + 1);
  REP(i, n) a[i + 1] = a[i] + v[i];
  REP(i, n + 1) a[i] = (a[i] - i + k) % k;
  map<int, int> mp;
  mp[0]++;
  ll ans = 0;
  REP(i, n) {
    if (i >= k - 1) mp[a[i - k + 1]]--;
    ans += mp[a[i + 1]];
    mp[a[i + 1]]++;
  }
  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 "bits/stdc++.h"

using namespace std;
using ll = long long;
#define REP(i, n) for (int i = 0; i < n; ++i)
#define ALL(v) v.begin(), v.end()

int main() {
  int n, k;
  cin >> n >> k;
  vector<int> v(n);
  REP(i, n) cin >> v[i];
  vector<ll> a(n + 1);
  REP(i, n) a[i + 1] = a[i] + v[i];
  REP(i, n + 1) a[i] = (a[i] - i + k) % k;
  map<int, int> mp;
  mp[0]++;
  ll ans = 0;
  REP(i, n) {
    if (i >= k - 1) mp[a[i - k + 1]]--;
    ans += mp[a[i + 1]];
    mp[a[i + 1]]++;
  }
  cout << ans << endl;
}

```