#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define INF 1LL<<62
#define inf 1000000007

int main() {
	ll n,k;
	cin>>n>>k;
	ll a[200010],b[200010];
	for(ll i=0;i<n;i++){
		cin>>a[i];
		a[i]-=1;
	}
	b[0]=0;
	for(ll i=1;i<=n;i++){
		b[i]=b[i-1]+a[i-1];
		b[i]%=k;
   // 	cout <<b[i];
	}
//	cout <<endl;
	map<ll,ll>ch;
	ll ans=0;
	for(ll i=0;i<=n;i++){
		if(i-k>=0){
		ll mae=b[i-k];
		ch[mae]--;
		}		
		ll now=b[i];
		ans+=ch[now];
		ch[now]++;
	}
	cout <<ans;
	// your code goes here
	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;
typedef long long ll;
#define INF 1LL<<62
#define inf 1000000007

int main() {
	ll n,k;
	cin>>n>>k;
	ll a[200010],b[200010];
	for(ll i=0;i<n;i++){
		cin>>a[i];
		a[i]-=1;
	}
	b[0]=0;
	for(ll i=1;i<=n;i++){
		b[i]=b[i-1]+a[i-1];
		b[i]%=k;
   // 	cout <<b[i];
	}
//	cout <<endl;
	map<ll,ll>ch;
	ll ans=0;
	for(ll i=0;i<=n;i++){
		if(i-k>=0){
		ll mae=b[i-k];
		ch[mae]--;
		}		
		ll now=b[i];
		ans+=ch[now];
		ch[now]++;
	}
	cout <<ans;
	// your code goes here
	return 0;
}
```