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

long long num[200010],out,k;
unordered_map < long long , long long > m;

int main()
{
	int n;
	cin>>n>>k;
//	vector < int > num(n + 1,0);
	for(int i = 1;i <= n;i++)
	{
		long long in;
		cin>>in;
		num[i] = (num[i - 1] + in) % k;
	} 
	
	for(int i = 0;i <= n;i++)
	{
		num[i] = ((num[i] - i) % k + k) % k;
		if(i >= k) m[num[i - k]]--;
		out += m[num[i]];
		m[num[i]]++; 
	}
	cout<<out;
	
	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;

long long num[200010],out,k;
unordered_map < long long , long long > m;

int main()
{
	int n;
	cin>>n>>k;
//	vector < int > num(n + 1,0);
	for(int i = 1;i <= n;i++)
	{
		long long in;
		cin>>in;
		num[i] = (num[i - 1] + in) % k;
	} 
	
	for(int i = 0;i <= n;i++)
	{
		num[i] = ((num[i] - i) % k + k) % k;
		if(i >= k) m[num[i - k]]--;
		out += m[num[i]];
		m[num[i]]++; 
	}
	cout<<out;
	
	return 0;
}

```