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=1e6+10;
const int MOD=1e9+7;
typedef long long ll;
ll a[N];
int n,m;
int main()
{
	cin>>n>>m;
	for(int i=1;i<=n;i++) cin>>a[i];
	int zh=0,fs=0;
	for(int i=1;i<=n;i++)
	{
		if(a[i]>0) zh++;
		else fs++;
	}
	ll sum=1;
	if((m&1)&&(zh==0))
	{
		sort(a+1,a+1+n,greater<int>());
		
		for(int i=1;i<=m;i++) sum=(sum*a[i])%MOD;
	//	cout<<sum<<endl;
	}
	else
	{
		sort(a+1,a+1+n,greater<int>());
		int l=1,r=n;
		while(m>0)
		{
			if(m&1) sum=(sum*a[l])%MOD,l++,m--;
			if(m>=2)
			{
				if(a[l]*a[l+1]>=a[r]*a[r-1]) 
				{
					sum=(sum*a[l]%MOD*a[l+1])%MOD;
					l+=2;
					m-=2;
				}
				else
				{
					sum=(sum*a[r]%MOD*a[r-1])%MOD;
					r-=2;
					m-=2;
					
				}
			}
			
		}
	}
	cout<<(sum%MOD+MOD)%MOD<<endl;
}