#include <bits/stdc++.h>
using namespace std;

int main()
{
	int64_t n, k;
	cin >> n >> k;
	vector<int64_t> as(n);
	for (auto &&a : as)
	{
		cin >> a;
	}

	for (auto &&a : as)
	{
		a--;
	}

	vector<int64_t> sum(n + 1, 0);
	for (int i = 0; i < n; i++)
	{
		sum[i + 1] = sum[i] + as[i];
	}

	int64_t ans = 0;

	map<int64_t, int64_t> mp;

	for (int i = 0; i <= n; i++)
	{
		if (k <= i)
		{
			mp[sum[i - k] % k]--;
		}
		ans += mp[sum[i] % k]++;
	}

	cout << ans << endl;

	return 0;
}
### Prompt

Please create a solution in Cpp 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;

int main()
{
	int64_t n, k;
	cin >> n >> k;
	vector<int64_t> as(n);
	for (auto &&a : as)
	{
		cin >> a;
	}

	for (auto &&a : as)
	{
		a--;
	}

	vector<int64_t> sum(n + 1, 0);
	for (int i = 0; i < n; i++)
	{
		sum[i + 1] = sum[i] + as[i];
	}

	int64_t ans = 0;

	map<int64_t, int64_t> mp;

	for (int i = 0; i <= n; i++)
	{
		if (k <= i)
		{
			mp[sum[i - k] % k]--;
		}
		ans += mp[sum[i] % k]++;
	}

	cout << ans << endl;

	return 0;
}
```