#include <iostream>
#include <algorithm>
#include <map>
const int maxN = 2e5 + 10;
using namespace std;

int n, k;
int a[maxN];
map<long long, long long> cnt;

int main()
{
	cin >> n >> k;
	cnt[0] = 1;

	long long ans = 0;
	for (long long i = 1; i <= n; ++i)
    {
        long long x;
        cin >> x;
		a[i] = (a[i - 1] + x - 1) % k;
		if (i >= k)
            cnt[a[i-k]]--;
		ans += cnt[a[i]]++;
	}

	cout << ans << '\n';

	return 0;
}

### Prompt

Your challenge is to write 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 <iostream>
#include <algorithm>
#include <map>
const int maxN = 2e5 + 10;
using namespace std;

int n, k;
int a[maxN];
map<long long, long long> cnt;

int main()
{
	cin >> n >> k;
	cnt[0] = 1;

	long long ans = 0;
	for (long long i = 1; i <= n; ++i)
    {
        long long x;
        cin >> x;
		a[i] = (a[i - 1] + x - 1) % k;
		if (i >= k)
            cnt[a[i-k]]--;
		ans += cnt[a[i]]++;
	}

	cout << ans << '\n';

	return 0;
}

```