#include <iostream>
#include <map>
using namespace std;
long long a[200010],sum[200010] = {},x[200010];
map<long long,long long> mp;
int main(){
	long long i,n,k;
	cin >> n >> k;
	for(i=0;i<n;i++){
		cin >> a[i];
		sum[i + 1] = sum[i] + a[i];
	}
	for(i=0;i<=n;i++){
		x[i] = sum[i]%k - i;
	}
	long long ans = 0;
	for(i=0;i<=n;i++){
		long long y = x[i];
		if(i>=k) mp[x[i - k]]--;
		if(mp.find(y)!=mp.end()){
			ans += mp[y];
		}
		if(mp.find(y + k)!=mp.end()){
			ans += mp[y + k];
		}
		mp[y]++;
	}
	cout << ans << endl;
}
### 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 <iostream>
#include <map>
using namespace std;
long long a[200010],sum[200010] = {},x[200010];
map<long long,long long> mp;
int main(){
	long long i,n,k;
	cin >> n >> k;
	for(i=0;i<n;i++){
		cin >> a[i];
		sum[i + 1] = sum[i] + a[i];
	}
	for(i=0;i<=n;i++){
		x[i] = sum[i]%k - i;
	}
	long long ans = 0;
	for(i=0;i<=n;i++){
		long long y = x[i];
		if(i>=k) mp[x[i - k]]--;
		if(mp.find(y)!=mp.end()){
			ans += mp[y];
		}
		if(mp.find(y + k)!=mp.end()){
			ans += mp[y + k];
		}
		mp[y]++;
	}
	cout << ans << endl;
}
```