#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int main(){
	ll n,k;
	cin>>n>>k;

	ll arr[n];
	for(ll i =0;i<n;i++)
		cin>>arr[i];

	ll s[n+1];
	s[0] = 0;

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

	map<ll,ll> m;
	m[0] = 1;

	ll ans = 0;
	for(ll j = 1;j <= n;j++){
		//find i such that (s[j] - j) %k = (s[i] - i)%k
		// j - k < i < j
		//cout<<s[j]<<endl;
		if(j - k >= 0)
			m[s[j-k]]--;

		ans+=m[s[j]];

		m[s[j]]++;
	}
	cout<<ans;
}
### Prompt

In cpp, your task is to solve 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;
int main(){
	ll n,k;
	cin>>n>>k;

	ll arr[n];
	for(ll i =0;i<n;i++)
		cin>>arr[i];

	ll s[n+1];
	s[0] = 0;

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

	map<ll,ll> m;
	m[0] = 1;

	ll ans = 0;
	for(ll j = 1;j <= n;j++){
		//find i such that (s[j] - j) %k = (s[i] - i)%k
		// j - k < i < j
		//cout<<s[j]<<endl;
		if(j - k >= 0)
			m[s[j-k]]--;

		ans+=m[s[j]];

		m[s[j]]++;
	}
	cout<<ans;
}
```