#include<bits/stdc++.h>
#define int long long 
using namespace std;
const int maxn=200000;
map<int,int> buc;
int n,k;
int a[maxn+5];
int Sub(int x,int y)
{
	x-=y;
	if(x<0) x+=k;
	return x;
}
signed main()
{
	scanf("%lld%lld",&n,&k);
	for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
	for(int i=1;i<=n;i++) a[i]=(a[i-1]+a[i])%k;
	buc[Sub(a[0],0)]++;
	int now=0,ans=0;
	for(int i=1;i<=n;i++)
	{
		while(now<i-k+1) buc[Sub(a[now],now%k)]--,now++;
		ans+=buc[Sub(a[i],i%k)];
		buc[Sub(a[i],i%k)]++;
	}
	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>
#define int long long 
using namespace std;
const int maxn=200000;
map<int,int> buc;
int n,k;
int a[maxn+5];
int Sub(int x,int y)
{
	x-=y;
	if(x<0) x+=k;
	return x;
}
signed main()
{
	scanf("%lld%lld",&n,&k);
	for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
	for(int i=1;i<=n;i++) a[i]=(a[i-1]+a[i])%k;
	buc[Sub(a[0],0)]++;
	int now=0,ans=0;
	for(int i=1;i<=n;i++)
	{
		while(now<i-k+1) buc[Sub(a[now],now%k)]--,now++;
		ans+=buc[Sub(a[i],i%k)];
		buc[Sub(a[i],i%k)]++;
	}
	printf("%lld\n",ans);
	return 0;
}
```