#include <bits/stdc++.h>

using namespace std;

const int N = 2e5+7;

int n, k;
int a[N], s[N];
long long res;
map<int, int> cnt;

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

### Prompt

Your task is to create a Cpp solution to 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 <bits/stdc++.h>

using namespace std;

const int N = 2e5+7;

int n, k;
int a[N], s[N];
long long res;
map<int, int> cnt;

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

```