# include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
map < int, set < int > > f; 
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);
	int n, k;
	long long ans = 0, cur = 0; 
	cin >> n >> k;
	f[0].insert(0);
	for(int i = 1, a; i <= n; i++){
		cin >> a; 
		cur = (cur + a - 1) % k; 
		int er = i - k; 
		while(f[cur].size() && *f[cur].begin() <= er){
			f[cur].erase(f[cur].begin());
		}
		ans += f[cur].size();
		f[cur].insert(i);
	}
	cout << ans << endl;
}
### 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 + 10;
map < int, set < int > > f; 
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);
	int n, k;
	long long ans = 0, cur = 0; 
	cin >> n >> k;
	f[0].insert(0);
	for(int i = 1, a; i <= n; i++){
		cin >> a; 
		cur = (cur + a - 1) % k; 
		int er = i - k; 
		while(f[cur].size() && *f[cur].begin() <= er){
			f[cur].erase(f[cur].begin());
		}
		ans += f[cur].size();
		f[cur].insert(i);
	}
	cout << ans << endl;
}
```