#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
const int N = 2e5;

int n,k;
map<int,int> ada;
int li[N+5];
int ps[N+5];

int main(){
	scanf("%d%d",&n,&k);
	ll ans = 0ll;
	ada[0] = 1;
	for(int i=1;i<=n;i++){
		if(i>=k){
			ada[ps[i-k]]--;
//			cout << "BUANG " << ps[i-k-1] << endl;
		}
		scanf("%d",&li[i]);
		li[i]--;
		li[i]%=k;
		ps[i] = (ps[i-1] + li[i])%k;
		ans += (ll) ada[ps[i]];
		ada[ps[i]]++;
//		cout << ">>> " << ps[i] << " " <<  ans << endl;
	}
	printf("%lld\n",ans);
	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<bits/stdc++.h>
using namespace std;

typedef long long ll;
const int N = 2e5;

int n,k;
map<int,int> ada;
int li[N+5];
int ps[N+5];

int main(){
	scanf("%d%d",&n,&k);
	ll ans = 0ll;
	ada[0] = 1;
	for(int i=1;i<=n;i++){
		if(i>=k){
			ada[ps[i-k]]--;
//			cout << "BUANG " << ps[i-k-1] << endl;
		}
		scanf("%d",&li[i]);
		li[i]--;
		li[i]%=k;
		ps[i] = (ps[i-1] + li[i])%k;
		ans += (ll) ada[ps[i]];
		ada[ps[i]]++;
//		cout << ">>> " << ps[i] << " " <<  ans << endl;
	}
	printf("%lld\n",ans);
	return 0;
}

```