#include <iostream>
#include <cstdio>
#include <map>
using namespace std;
typedef long long ll;

ll n, k, t, ans, a[200005];
map<ll, ll> mp;
int main() {
	cin >> n >> k;
	mp[0] = 1;
	for(ll i=1; i<=n; i++) {
		if(i>=k) mp[a[i-k]]--;
		scanf("%lld", &t);
		a[i] = (a[i-1] + t-1) % k;
		ans += mp[a[i]];
		mp[a[i]]++;
	}
	cout << ans;
	return 0;
}
### 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 <iostream>
#include <cstdio>
#include <map>
using namespace std;
typedef long long ll;

ll n, k, t, ans, a[200005];
map<ll, ll> mp;
int main() {
	cin >> n >> k;
	mp[0] = 1;
	for(ll i=1; i<=n; i++) {
		if(i>=k) mp[a[i-k]]--;
		scanf("%lld", &t);
		a[i] = (a[i-1] + t-1) % k;
		ans += mp[a[i]];
		mp[a[i]]++;
	}
	cout << ans;
	return 0;
}
```