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

#define endl '\n'

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

    long long n, k, ans=0; cin >> n >> k;
    long long ac[n+1]; ac[0] = 0;
    map<long long, long long> freq;
    freq[0] = 1;
    for (int i=1; i<=n; i++){
        if (i >= k) freq[(ac[i-k] - i + k)%k]--;
        cin >> ac[i];
        if (k == 1 && ac[i]%k == 1) ans++;
        ac[i] += ac[i-1];
        ans += freq[(ac[i] - i)%k]++;
    }
    cout << ans << endl;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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 endl '\n'

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

    long long n, k, ans=0; cin >> n >> k;
    long long ac[n+1]; ac[0] = 0;
    map<long long, long long> freq;
    freq[0] = 1;
    for (int i=1; i<=n; i++){
        if (i >= k) freq[(ac[i-k] - i + k)%k]--;
        cin >> ac[i];
        if (k == 1 && ac[i]%k == 1) ans++;
        ac[i] += ac[i-1];
        ans += freq[(ac[i] - i)%k]++;
    }
    cout << ans << endl;
}
```