#include <bits/stdc++.h>
using namespace std;
int main(){
	int n, k; cin >> n >> k;
	vector<int> a(n), to(n + 1);
	for(int i = 0; i < n; i++) cin >> a[i];
	if(k == 1){
		cout << 0 << endl;
		return 0;
	}
	long long ans = 0, sum = 0;
	map<int, int> cnt;
	cnt[0] = 1;
	to[0] = 0;
	for(int i = 1; i <= n; i++){
		if(i >= k) cnt[to[i - k]]--;
		sum += a[i - 1];
		sum %= k;
		int val = (sum - i) % k;
		val += k; val %= k;
		ans += cnt[val];
		cnt[val]++;
		to[i] = val;
	}
	cout << ans << endl;
	return 0;
}

### Prompt

Generate 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;
int main(){
	int n, k; cin >> n >> k;
	vector<int> a(n), to(n + 1);
	for(int i = 0; i < n; i++) cin >> a[i];
	if(k == 1){
		cout << 0 << endl;
		return 0;
	}
	long long ans = 0, sum = 0;
	map<int, int> cnt;
	cnt[0] = 1;
	to[0] = 0;
	for(int i = 1; i <= n; i++){
		if(i >= k) cnt[to[i - k]]--;
		sum += a[i - 1];
		sum %= k;
		int val = (sum - i) % k;
		val += k; val %= k;
		ans += cnt[val];
		cnt[val]++;
		to[i] = val;
	}
	cout << ans << endl;
	return 0;
}

```