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

#define i64 long long int
#define ran 202202

int n, k;
int s[ran];
map<int, vector<int> > v;
map<int, int> it;

int main() {
	scanf("%d%d", &n, &k);
	
	i64 ans = 0LL;
	
	s[0] = 0;
	v[0].push_back(0);
	for(int i=1;i<=n;i++) {
		int x;
		scanf("%d", &x);
		s[i] = (s[i-1]+x-1)%k;
		
		int cur = s[i];
		v[cur].push_back(i);
		while(v[cur][it[cur]] < i-(k-1)) it[cur]++;
		ans += (int)v[cur].size() - it[cur] - 1;
	}
	
	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;

#define i64 long long int
#define ran 202202

int n, k;
int s[ran];
map<int, vector<int> > v;
map<int, int> it;

int main() {
	scanf("%d%d", &n, &k);
	
	i64 ans = 0LL;
	
	s[0] = 0;
	v[0].push_back(0);
	for(int i=1;i<=n;i++) {
		int x;
		scanf("%d", &x);
		s[i] = (s[i-1]+x-1)%k;
		
		int cur = s[i];
		v[cur].push_back(i);
		while(v[cur][it[cur]] < i-(k-1)) it[cur]++;
		ans += (int)v[cur].size() - it[cur] - 1;
	}
	
	cout<<ans<<endl;
	
	return 0;
}
```