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;
int mod=1e9+7;
long long a[200001],n,m;
long long read(){
    long long ans=0;
    char last=' ',ch=getchar();
    while(ch<'0' || ch>'9')last=ch,ch=getchar();
    while(ch>='0' && ch<='9')ans=ans*10+ch-'0',ch=getchar();
    if(last=='-')ans=-ans;
    return ans;
}
int main()
{
	n=read(),m=read();
	for(int i=0;i<n;i++)a[i]=read();
	sort(a,a+n);
	int l=0,r=n-1,w=1; 
	long long ans=1;
	if(m&1)
	{	
		ans=a[r--];
		m--;
		w=(ans<0?-1:1);
	}
	while(m)
	{
		long long x=a[l]*a[l+1],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;
		m-=2;
	}
	printf("%lld",(ans%mod+mod)%mod);
}