#include <bits/stdc++.h>
using namespace std;

int main(){
	int N,K;
	cin >> N >> K;
	vector<int> A(N);
	for(auto &i:A)cin >> i;
	vector<long long> S(N+1,0);
	for(int i=0;i<N;i++)S[i+1]=(S[i]+(A[i]-1))%K;
	
	long long ans=0;
	map<long long,vector<int>> m;
	
	for(int i=0;i<N+1;i++){
		m[S[i]].push_back(i);
	}
	
	for(auto p:m){
		auto v=p.second;
		for(int i=0;i<v.size();i++){
			ans+=(int)(lower_bound(v.begin(),v.end(),v[i]+K)-lower_bound(v.begin(),v.end(),v[i]))-1;
		}
	}
	cout << ans << endl;
	return 0;
}
### Prompt

Your challenge is to write 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;

int main(){
	int N,K;
	cin >> N >> K;
	vector<int> A(N);
	for(auto &i:A)cin >> i;
	vector<long long> S(N+1,0);
	for(int i=0;i<N;i++)S[i+1]=(S[i]+(A[i]-1))%K;
	
	long long ans=0;
	map<long long,vector<int>> m;
	
	for(int i=0;i<N+1;i++){
		m[S[i]].push_back(i);
	}
	
	for(auto p:m){
		auto v=p.second;
		for(int i=0;i<v.size();i++){
			ans+=(int)(lower_bound(v.begin(),v.end(),v[i]+K)-lower_bound(v.begin(),v.end(),v[i]))-1;
		}
	}
	cout << ans << endl;
	return 0;
}
```