#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,k,s[200001],a,L,cnt,ans;
map<ll,ll>mp;
int main(void){
	cin>>n>>k;
	for(int i=0;i<n;i++){
		cin>>a;
		s[i+1]=s[i]+a;
	}
	for(ll i=0;i<=n;i++){
		s[i]-=i;
		s[i]%=k;
		s[i]=(s[i]+k)%k;
	}
	n++;
	for(int i=0;i<min(n,k);i++){
		ans+=mp[s[i]];
		mp[s[i]]++;
	}
	for(int i=0;i<n-min(n,k);i++){
		mp[s[i]]--;
		ans+=mp[s[i+min(n,k)]];
		mp[s[i+min(n,k)]]++;
	}
	cout<<ans<<endl;
}
### Prompt

Please formulate 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;
ll n,k,s[200001],a,L,cnt,ans;
map<ll,ll>mp;
int main(void){
	cin>>n>>k;
	for(int i=0;i<n;i++){
		cin>>a;
		s[i+1]=s[i]+a;
	}
	for(ll i=0;i<=n;i++){
		s[i]-=i;
		s[i]%=k;
		s[i]=(s[i]+k)%k;
	}
	n++;
	for(int i=0;i<min(n,k);i++){
		ans+=mp[s[i]];
		mp[s[i]]++;
	}
	for(int i=0;i<n-min(n,k);i++){
		mp[s[i]]--;
		ans+=mp[s[i+min(n,k)]];
		mp[s[i+min(n,k)]]++;
	}
	cout<<ans<<endl;
}
```