#include <iostream>
#include <map>

using namespace std;

typedef map<int, int> mii;

int main() {
    ios::sync_with_stdio(false);

    int n, k;
    cin >> n >> k;

    long long ans = 0;
    mii c;
    int ps[n+1];
    ps[0] = 0;
    c[0]++;
    for (int i = 1; i <= n; i++) {
        int a;
        cin >> a;
        a = (a + k - 1) % k;

        if (i >= k) {
            c[ps[i-k]]--;
        }

        ps[i] = (ps[i-1] + a) % k;
        ans += c[ps[i]];

        c[ps[i]]++;
    }

    cout << ans << 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;

typedef map<int, int> mii;

int main() {
    ios::sync_with_stdio(false);

    int n, k;
    cin >> n >> k;

    long long ans = 0;
    mii c;
    int ps[n+1];
    ps[0] = 0;
    c[0]++;
    for (int i = 1; i <= n; i++) {
        int a;
        cin >> a;
        a = (a + k - 1) % k;

        if (i >= k) {
            c[ps[i-k]]--;
        }

        ps[i] = (ps[i-1] + a) % k;
        ans += c[ps[i]];

        c[ps[i]]++;
    }

    cout << ans << endl;

    return 0;
}

```