#include <bits/stdc++.h>
using namespace std ;
 
const long long mod = 1e9 + 7 ;
 
vector <pair<int,int> > g[312345];
long long a[312345];

int n,k;
map<long long, long long> mp;

int main ( ) {

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

Create a solution in Cpp for 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 long long mod = 1e9 + 7 ;
 
vector <pair<int,int> > g[312345];
long long a[312345];

int n,k;
map<long long, long long> mp;

int main ( ) {

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