#include <iostream>
#include <map>
using namespace std;

const int N = 2e5 + 10;

int n, k, a[N], cum[N];

int main() {
    cin >> n >> k;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        a[i] += k-1;
        a[i] %= k;
        cum[i+1] = (a[i] + cum[i]) % k;
    }
    long long res = 0;
    map<int,int> cnt;
    for (int i = 0; i <= n; i++)  {
        if (i >= k) cnt[cum[i-k]]--;
        res += cnt[cum[i]]++;
    }
    cout << res << 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;

const int N = 2e5 + 10;

int n, k, a[N], cum[N];

int main() {
    cin >> n >> k;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        a[i] += k-1;
        a[i] %= k;
        cum[i+1] = (a[i] + cum[i]) % k;
    }
    long long res = 0;
    map<int,int> cnt;
    for (int i = 0; i <= n; i++)  {
        if (i >= k) cnt[cum[i-k]]--;
        res += cnt[cum[i]]++;
    }
    cout << res << endl;

    return 0;
}


```