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;
long long mod=1e9+7;
long long n,m;
long long a[200005];
bool cmp(int x,int y)
{
	return abs(x)<abs(y);
 } 
 int main()
 {
 	int pn=0,nn=0;
 	cin>>n>>m;
 	for(int i=1;i<=n;i++)
 	{
 		cin>>a[i];
 		if(a[i]>=0)
 			pn++;
 		else 
 			nn++;
	 }
	 int l=1,r=n;
	 long long ans=1;
	 if(!pn&&m%2==1)
	 {
	 	sort(a+1,a+1+n,cmp);
	 	for(int i=1;i<=m;i++)
	 		ans=a[i]*ans%mod;
	 }
	 else 
	 {
	 	sort(a+1,a+1+n,greater< int >());
	 	while(m)
	 	{
	 		if(m%2==1)
	 		{
	 			ans=ans*a[l]%mod;
	 			l++;
	 			m--;
			 }
			 else 
			 {
			 	if(a[l]*a[l+1]>=a[r]*a[r-1])
			 	{
			 		ans=ans*a[l]%mod*a[l+1]%mod;
			 		l+=2;
			 		m-=2;
				 }
				 else 
				{
					ans=ans*a[r]%mod*a[r-1]%mod;
					r-=2;
					m-=2;
				}
			 }
		 }
	 }
	cout << (ans % mod + mod) % mod << endl;
 }