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 int N=2e5+20,MOD=1e9+7;

int n,k;
long long a[N],ans=1;

int main()
{
	scanf("%d%d",&n,&k);
	for(int i=0;i<n;i++) scanf("%lld",&a[i]);

	sort(a,a+n);
	int l=0,r=n-1,sign=1;
	if(k&1)
	{
		ans=a[r--];
		k--;
		if(ans<0) sign=-1;
	}

	while(k)
	{
		long long x=a[l]*a[l+1],y=a[r]*a[r-1];
		if(x*sign>y*sign)
		{
			x%=MOD;
			ans=(ans*x)%MOD;
			l+=2;
		}
		else
		{
			y%=MOD;
			ans=(ans*y)%MOD;
			r-=2;
		}
		k-=2;
	}

	printf("%lld",(ans+MOD)%MOD);
}