#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
map<ll,ll>m;
const int N = 2e5;
ll sum[N+100];
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	ll n,k;
	ll ans = 0;
	cin >> n >> k;
	m[0] = 1;
	for(ll i=1;i<=n;i++){
		ll a;
		cin >> a;
		sum[i] = (sum[i-1]+a)%k;
		ans += (m[(sum[i]-(i)%k+k)%k]);
		m[(sum[i]-(i)%k+k)%k]++;
		if(i-k+1>=0){
			m[(sum[i-k+1]-(i-k+1)%k+k)%k]--;
		}
	}
	if(k==1){
		cout << "0\n";
	}
	else cout << ans << "\n";
}

### Prompt

Generate 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;
map<ll,ll>m;
const int N = 2e5;
ll sum[N+100];
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	ll n,k;
	ll ans = 0;
	cin >> n >> k;
	m[0] = 1;
	for(ll i=1;i<=n;i++){
		ll a;
		cin >> a;
		sum[i] = (sum[i-1]+a)%k;
		ans += (m[(sum[i]-(i)%k+k)%k]);
		m[(sum[i]-(i)%k+k)%k]++;
		if(i-k+1>=0){
			m[(sum[i-k+1]-(i-k+1)%k+k)%k]--;
		}
	}
	if(k==1){
		cout << "0\n";
	}
	else cout << ans << "\n";
}

```