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;
const long long maxn=2e5+5;
const long long inf=0x3f3f3f3f;
const long long mod=1e9+7;
long long a[maxn],ans=1,w=1; 
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	long long n,k;
	cin>>n>>k;
	long long l=1,r=n;
	for(long long i=1;i<=n;i++)
		cin>>a[i];
	sort(a+1,a+n+1);
	long long ans=1;
	if(k&1)
	{
		ans=a[r--];
		k--;
		w=(ans<0?-1:1); 
	} 
	while(k)
	{
		long long x=a[l]*a[l+1];
		long long y=a[r]*a[r-1];
		if(x*w>y*w)
		{
			ans=ans*(x%mod)%mod;
			l+=2;
		}
		else
		{
			ans=ans*(y%mod)%mod;
			r-=2;
		}
		k-=2;
	}
	cout<<(ans%mod+mod)%mod<<endl;
	return 0;
}


