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

int n, k;
ll A[200005], S[200005];

int main() {
    cin >> n >> k;
    for (int i = 0; i < n; i++) {
        cin >> A[i];
        A[i]--;
        S[i + 1] = (S[i] + A[i] + k) % k;
    }

    ll ans = 0;
    
    map<int, int> mp;

    for(int i = 0; i <= n; i++){
        if (i - k >= 0) mp[S[i - k]]--;
        ans += mp[S[i]];
        mp[S[i]]++;
    }
    cout << ans << endl;
    return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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;

int n, k;
ll A[200005], S[200005];

int main() {
    cin >> n >> k;
    for (int i = 0; i < n; i++) {
        cin >> A[i];
        A[i]--;
        S[i + 1] = (S[i] + A[i] + k) % k;
    }

    ll ans = 0;
    
    map<int, int> mp;

    for(int i = 0; i <= n; i++){
        if (i - k >= 0) mp[S[i - k]]--;
        ans += mp[S[i]];
        mp[S[i]]++;
    }
    cout << ans << endl;
    return 0;
}
```