#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> P;

int main(){
	int N, K; cin >> N >> K;
	ll A[N];
	for(int i=0; i<N; i++){ cin >> A[i]; A[i]--;}
	ll sum[N];
	sum[0] = A[0]%K;
	ll ans = 0;
	map<ll, ll> m;
	m[0]++;
	ans += m[sum[0]];
	m[sum[0]]++;
	for(int i=1; i<N; i++){
		sum[i] = (sum[i-1] + A[i]) % K;
		if(i - K + 1 >= 0){
			if(i-K+1 == 0) m[0]--;
			else m[sum[i-K]]--;
		}
		ans += m[sum[i]];
		m[sum[i]]++;
	}
	if(K==1) cout << 0 << endl;
	else 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;
typedef long long ll;
typedef pair<int, int> P;

int main(){
	int N, K; cin >> N >> K;
	ll A[N];
	for(int i=0; i<N; i++){ cin >> A[i]; A[i]--;}
	ll sum[N];
	sum[0] = A[0]%K;
	ll ans = 0;
	map<ll, ll> m;
	m[0]++;
	ans += m[sum[0]];
	m[sum[0]]++;
	for(int i=1; i<N; i++){
		sum[i] = (sum[i-1] + A[i]) % K;
		if(i - K + 1 >= 0){
			if(i-K+1 == 0) m[0]--;
			else m[sum[i-K]]--;
		}
		ans += m[sum[i]];
		m[sum[i]]++;
	}
	if(K==1) cout << 0 << endl;
	else cout << ans << endl;
	return 0;
}

```