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

#pragma GCC optimize ("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse4")
#include"bits/stdc++.h"
using namespace std;
typedef long long ll;
#define int ll
#define sz(x) (int)(x).size();
#define all(x) x.begin(), x.end()
#define trav(i,a) for(auto &i:a) 
inline int in(){int x;scanf("%lld",&x);return x;}
constexpr int mod=1e9+7;
int32_t main()
{
	
	int n=in();int k=in();
	vector<int> a(n);
	trav(i,a)i=in();sort(all(a));
	int l=0,r=n-1;
	int ans=1;
	if(k&1)
	{
		if(a[n-1]<0)
		{
			for(int i=n-1;i>=n-k;i--)
			{
				ans*=a[i];
				ans%=mod;
			}
			if(ans<0)cout<<(ans+mod)%mod;
			else cout<<ans%mod;
			return 0;
		}
		r--;k--;
	}
	
	while(k)
	{
		int lp=a[l]*a[l+1];
		int rp=a[r]*a[r-1];
		if(lp>rp)l+=2;
		else r-=2;
		
		k-=2;
	}

	for(int i=0;i<l;i++)
	{
		ans*=a[i];
		ans%=mod;
	}
	for(int i=r+1;i<n;i++){ans*=a[i];ans%=mod;}
	
	if(ans<0){ans+=mod;cout<<ans%mod;}
	else cout<<ans%mod;
	
	
}