#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,k,a[200010],s[200010];
map<ll,ll> cnt;
ll pmod(ll x){
	return(x%k+k)%k;
}
int main(){
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		scanf("%lld",&a[i]);
	}
	for(int i=1;i<=n;i++){
		s[i]=s[i-1]+a[i];
	}
	ll ans=0;
	for(int i=n;i>=1;i--){
		cnt[(s[i]-i)%k]++;
		if(i+k-1<=n){
			int tt=i+k-1;
			cnt[(s[tt]-tt)%k]--;
		}
		ll tmp=(s[i-1]-i+1ll)%k;
		ans+=cnt[tmp];
	}
	cout<<ans<<endl;
	return 0;
}
### Prompt

Please formulate 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;
ll n,k,a[200010],s[200010];
map<ll,ll> cnt;
ll pmod(ll x){
	return(x%k+k)%k;
}
int main(){
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		scanf("%lld",&a[i]);
	}
	for(int i=1;i<=n;i++){
		s[i]=s[i-1]+a[i];
	}
	ll ans=0;
	for(int i=n;i>=1;i--){
		cnt[(s[i]-i)%k]++;
		if(i+k-1<=n){
			int tt=i+k-1;
			cnt[(s[tt]-tt)%k]--;
		}
		ll tmp=(s[i-1]-i+1ll)%k;
		ans+=cnt[tmp];
	}
	cout<<ans<<endl;
	return 0;
}
```