Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

* 1 \leq K \leq N \leq 2\times 10^5
* |A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 \ldots A_N


Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Examples

Input

4 2
1 2 -3 -4


Output

12


Input

4 3
-1 -2 -3 -4


Output

1000000001


Input

2 1
-1 1000000000


Output

1000000000


Input

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1


Output

999983200
#include<bits/stdc++.h>
using namespace std;
long long int a[200005];
const int mod=1e9+7;
int main()
{
	int n,m,i;
  scanf("%d %d",&n,&m);
  for(i=1;i<=n;i++)
  {
  	scanf("%lld",&a[i]);
  }
  long long int ans=1;
  sort(a+1,a+1+n);
  if(m==n||a[n]<0)
  {
  	if(m%2==0)
  	{
  	  for(i=1;i<=m;i++)
  	  ans=(ans*a[i])%mod;
	}
	else
	{
		for(i=n-m+1;i<=n;i++)
		ans=(ans*a[i])%mod;
	}
  }
  else
  {
  	int l=1,r=n;
  	if(m%2==1)
  	{
  	  ans=(ans*a[n])%mod;
	  r--;	
	  m--;
	}
	while(m)
	{
		if(a[l]*a[l+1]>a[r]*a[r-1])
		{
			ans=(ans*a[l]%mod*a[l+1]%mod)%mod;
			l+=2;
			m-=2;
		}
		else
		{
			ans=(ans*a[r]%mod*a[r-1]%mod)%mod;
			r-=2;
			m-=2;
		}
	}
	
  }
  ans=(ans%mod+mod)%mod;
  printf("%lld",ans);
} 