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

ll a[200010], sum[200010];

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

Your challenge is to write 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 <map>
#define ll long long
using namespace std;

ll a[200010], sum[200010];

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