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<iostream>
#include<vector>
#include<algorithm>
#define M 1000000007
using namespace std;

long long mod(long long a, long long b)
{
    long long r = a % b;
    return r < 0 ? r + b : r;
}

int main()
{
		int n,k,val=0;
		cin>>n>>k;
		std::vector<long long> v;
		v.resize(n);

		for(int i=0;i<n;i++)
		{
			cin>>v[i];
		}

		sort(v.begin() , v.begin()+n);

		long long product=1;
		int start = 0 , end = n-1;

		if(v[end]<0)
		{	
			if(k&1)
			{
				for(int i=0;i<k;i++)
				{
					product = mod(mod(product,M) * mod(v[end-i],M) , M);
				}
				cout<<product<<endl;
				val=1;
			}
			else
			{
				for(int i=0;i<k;i++)
				{
					product = mod(mod(product,M) * mod(v[i],M) , M);
				}
				cout<<product<<endl;
				val=1;
			}
		}

		while(k>0)
		{
			if(k&1)
			{	
				product = mod(mod(product,M) * mod(v[end],M) , M);
				end--;
				k--;
			}
			else
			{	
				long long temp1 = v[start]*v[start+1];
				long long temp2 = v[end]*v[end-1];

				product = mod(mod(product,M) * mod(max(temp1,temp2),M),M);
				if(temp1>temp2)	start += 2;
				else end -= 2;
				k -= 2;
			}
		}
		if(val==0)
		    cout<<product<<endl;
}