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

const int MOD = (int)1e9+7;

int main(){
	int N;
	long long K;
	cin >> N >> K;
	vector<long long> A(N);
	for(int i=0;i<N;i++){
		cin >> A.at(i);
		A.at(i)+=K-1;
	}

	vector<long long> sum(N+1,0);
	for(int i=0;i<N;i++)	sum.at(i+1)=sum.at(i)+A.at(i);

	map<long long,long long> mp;
	long long ans=0;
	mp[0]++;
	for(int i=1;i<=N;i++){
		long long x=sum.at(i)%K;
		if(i-K>=0)	mp[sum.at(i-K)%K]--;
		if(mp.count(x))	ans+=mp.at(x);
		mp[x]++;
	}
	cout << ans << endl;

	return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;

const int MOD = (int)1e9+7;

int main(){
	int N;
	long long K;
	cin >> N >> K;
	vector<long long> A(N);
	for(int i=0;i<N;i++){
		cin >> A.at(i);
		A.at(i)+=K-1;
	}

	vector<long long> sum(N+1,0);
	for(int i=0;i<N;i++)	sum.at(i+1)=sum.at(i)+A.at(i);

	map<long long,long long> mp;
	long long ans=0;
	mp[0]++;
	for(int i=1;i<=N;i++){
		long long x=sum.at(i)%K;
		if(i-K>=0)	mp[sum.at(i-K)%K]--;
		if(mp.count(x))	ans+=mp.at(x);
		mp[x]++;
	}
	cout << ans << endl;

	return 0;
}

```