#include<iostream>
#include<map>
using namespace std;
typedef long long LL;
const int N = 200010;
LL a[N];
LL x[N];
LL sum[N];
map<LL,int> m;
int main(){
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int n,k;
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		cin>>a[i];
		sum[i]=sum[i-1]+a[i];
		x[i]=(sum[i]-i+k)%k;
	}
	LL ans=0;
	m[0]=1;
	for(int i=1;i<=min(n,k-1);i++){
		ans+=m[x[i]];
		m[x[i]]++;
	}
	for(int i=k;i<=n;i++){
		m[x[i-k]]--;
		ans+=m[x[i]];
		m[x[i]]++;
	}
	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<iostream>
#include<map>
using namespace std;
typedef long long LL;
const int N = 200010;
LL a[N];
LL x[N];
LL sum[N];
map<LL,int> m;
int main(){
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int n,k;
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		cin>>a[i];
		sum[i]=sum[i-1]+a[i];
		x[i]=(sum[i]-i+k)%k;
	}
	LL ans=0;
	m[0]=1;
	for(int i=1;i<=min(n,k-1);i++){
		ans+=m[x[i]];
		m[x[i]]++;
	}
	for(int i=k;i<=n;i++){
		m[x[i-k]]--;
		ans+=m[x[i]];
		m[x[i]]++;
	}
	cout<<ans<<endl;
	return 0;
}
```