#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < n; i++)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const ll MAX_N = 200005;
ll A[MAX_N],S[MAX_N];
map<ll,ll> c;

int main()
{
	ll N,K;
	cin >> N >> K;
	rep(i,N)
	{
		cin >> A[i];
		A[i]--;
		S[i+1] = (S[i] + A[i]) % K;
	}
	ll ans = 0;
	for (ll j = 0; j <= N; ++j)
	{
		ans += c[S[j]];
		if (j >= K-1) c[S[j-K+1]]--;
		c[S[j]]++;
	}
	cout << ans << endl;
	return 0;
}
### Prompt

In cpp, your task is to solve 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>
#define rep(i,n) for(int i = 0; i < n; i++)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const ll MAX_N = 200005;
ll A[MAX_N],S[MAX_N];
map<ll,ll> c;

int main()
{
	ll N,K;
	cin >> N >> K;
	rep(i,N)
	{
		cin >> A[i];
		A[i]--;
		S[i+1] = (S[i] + A[i]) % K;
	}
	ll ans = 0;
	for (ll j = 0; j <= N; ++j)
	{
		ans += c[S[j]];
		if (j >= K-1) c[S[j-K+1]]--;
		c[S[j]]++;
	}
	cout << ans << endl;
	return 0;
}
```