#include <iostream>
#include <map>
using namespace std;

long long mod(long long a, long long m) {
	a %= m;
	return a >= 0 ? a : a+m;
}

int main() {
	long long n, k;
	cin >> n >> k;
	long long ans = 0, S[n+1], x[n+1];
	map<long long, int> mp;
	S[0] = 0, x[0] = 0;
	mp[0]++;
	for (int i = 1; i <= n; i++) {
		long long a;
		cin >> a;
		S[i] = mod(S[i-1] + a, k);
		x[i] = mod(S[i] - i, k);
		if (i-k >= 0) mp[x[i-k]]--;
		ans += mp[x[i]];
		mp[x[i]]++;
	}
	cout << ans << endl;
	return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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;

long long mod(long long a, long long m) {
	a %= m;
	return a >= 0 ? a : a+m;
}

int main() {
	long long n, k;
	cin >> n >> k;
	long long ans = 0, S[n+1], x[n+1];
	map<long long, int> mp;
	S[0] = 0, x[0] = 0;
	mp[0]++;
	for (int i = 1; i <= n; i++) {
		long long a;
		cin >> a;
		S[i] = mod(S[i-1] + a, k);
		x[i] = mod(S[i] - i, k);
		if (i-k >= 0) mp[x[i-k]]--;
		ans += mp[x[i]];
		mp[x[i]]++;
	}
	cout << ans << endl;
	return 0;
}
```