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;
#define  ft  ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define  ll  long long
const int N=2e5+3;
ll M=1e9+7;
ll a[N];
int main()
{
    ft
    ll i,j,n,k,l,r,s=1;
    cin>>n>>k;
    for(i=0;i<n;i++)
    {
        cin>>a[i];
    }
    sort(a,a+n);
    if(k%2==1)
    {
        if(a[n-1]==0)
        {
            cout<<"0\n";
            return 0;
        }
        else if(a[n-1]<0)
        {
            for(i=n-1;i>=(n-k);i--)
            {
                s=(s*(a[i]+M))%M;
            }
            cout<<s<<"\n";
            return 0;
        }
        else
        {
            s=(s*(a[n-1]+M))%M;
            n--,k--;
        }
    }
    l=0,r=n-1;
    while(k>0)
    {
        if((a[l]*a[l+1])>(a[r]*a[r-1]))
        {
            s=(s*(a[l]+M))%M;
            s=(s*(a[l+1]+M))%M;
            l+=2;
        }
        else
        {
            s=(s*(a[r]+M))%M;
            s=(s*(a[r-1]+M))%M;
            r-=2;
        }
        k-=2;
    }
    cout<<s<<"\n";
    return 0;
}