#include <bits/stdc++.h>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;

int main(){
	int n;
	ll k;
	cin >> n >> k;
	ll a[n];
	for(int i=0; i<n; i++) cin >> a[i];

	ll s[n+1];
	s[0]=0;
	for(int i=0; i<n; i++) s[i+1]=s[i]+a[i];
	for(int i=0; i<=n; i++) s[i]=(s[i]-i)%k;

	map<ll, ll> cnt;
	ll ans=0;
	for(int i=0; i<=n; i++){
		cnt[s[i]]++;
		if(i>=k) cnt[s[i-k]]--;
		ans+=cnt[s[i]]-1;
	}
	cout << ans << endl;
	return 0;
}
### Prompt

Please create a solution in CPP 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 unsigned long long ull;
typedef long long ll;

int main(){
	int n;
	ll k;
	cin >> n >> k;
	ll a[n];
	for(int i=0; i<n; i++) cin >> a[i];

	ll s[n+1];
	s[0]=0;
	for(int i=0; i<n; i++) s[i+1]=s[i]+a[i];
	for(int i=0; i<=n; i++) s[i]=(s[i]-i)%k;

	map<ll, ll> cnt;
	ll ans=0;
	for(int i=0; i<=n; i++){
		cnt[s[i]]++;
		if(i>=k) cnt[s[i-k]]--;
		ans+=cnt[s[i]]-1;
	}
	cout << ans << endl;
	return 0;
}
```