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;
typedef long long ll;
ll n,k,ans;
ll a[200100];
ll mod=1e9+7;
int main()
{
	cin>>n>>k;
	for(int i=1;i<=n;i++)  scanf("%lld",&a[i]);
	sort(a+1,a+1+n);
	bool pd=0;
	ll l=1,r=n;
	ans=1;
	if(k&1)
	{
		if(a[n]<0)
		{
		  for(int i=1;i<=k;i++)  
		  ans=ans*a[n-i+1]%mod;	
		  pd=1;
		}
		else 
		{
			ans=a[n];
			r--;
		} 
		k--;
	}
	
	if(!pd)
	while(k)
	{
		ll aa=a[l]*a[l+1];
		ll bb=a[r]*a[r-1];
		if(aa>bb)  ans=ans*(aa%mod)%mod,l+=2;
		else       ans=ans*(bb%mod)%mod,r-=2;
		k-=2;       
	}
	cout<<(ans+mod)%mod<<endl;
	return 0;
}