#include <iostream>
#include <map>
#include <vector>

using namespace std;

int main() {
    int n, k;
    cin >> n >> k;

    vector<long long> a(n + 1, 0);
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        a[i] += a[i - 1];
    }

    long long res = 0;

    map<long long, int> m;
    m[0]++;
    for (int i = 1, j = 1 - k; i <= n; i++, j++) {
        if (j >= 0) {
            m[(a[j] - j) % k]--;
        }
        res += m[(a[i] - i) % k];
        m[(a[i] - i) % k]++;
    }

    cout << res << endl;
}

### Prompt

In cpp, your task is to solve 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>
#include <vector>

using namespace std;

int main() {
    int n, k;
    cin >> n >> k;

    vector<long long> a(n + 1, 0);
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        a[i] += a[i - 1];
    }

    long long res = 0;

    map<long long, int> m;
    m[0]++;
    for (int i = 1, j = 1 - k; i <= n; i++, j++) {
        if (j >= 0) {
            m[(a[j] - j) % k]--;
        }
        res += m[(a[i] - i) % k];
        m[(a[i] - i) % k]++;
    }

    cout << res << endl;
}

```