#include<bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

int main() {
    int n, k;
    cin >> n >> k;
    vector<int> A(n);
    rep(i, n) cin >> A[i];
    vector<int> S(n+1);
    S[0] = 0;
    rep(i, n) S[i+1] = (S[i] + A[i] - 1) % k;
    map<int, int> mp;
    ll ans = 0;
    for (int i = 0; i <= n; ++i) {
        ans += mp[S[i]];
        mp[S[i]]++;
        if (i >= k-1) mp[S[i-(k-1)]]--; 
    }
    cout << ans << endl;
    return 0;
}
### Prompt

Please formulate 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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

int main() {
    int n, k;
    cin >> n >> k;
    vector<int> A(n);
    rep(i, n) cin >> A[i];
    vector<int> S(n+1);
    S[0] = 0;
    rep(i, n) S[i+1] = (S[i] + A[i] - 1) % k;
    map<int, int> mp;
    ll ans = 0;
    for (int i = 0; i <= n; ++i) {
        ans += mp[S[i]];
        mp[S[i]]++;
        if (i >= k-1) mp[S[i-(k-1)]]--; 
    }
    cout << ans << endl;
    return 0;
}
```