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 ll long long
#define bada LLONG_MAX
#define chota LLONG_MIN
#define vl vector<ll>
#define pb push_back
#define mod 1000000007
int main()
{
    int n,k;
    cin>>n>>k;

    ll a[n];

    for(int i=0;i<n;i++)
         cin>>a[i];

    sort(a,a+n);
    reverse(a,a+n);

    int neg=1;
    int i=0,j=n-1;
    vl ans;
    if(k&1)
    {
        if(a[0]<0)
        {
            ans.pb(a[0]);
            neg=-1;
        }
        else
            ans.pb(a[0]);
       i=1;
    }
    while(ans.size()<k)
    {
        if(neg*a[i]*a[i+1]<neg*a[j]*a[j-1])
        {
            ans.pb(a[j]);
            ans.pb(a[j-1]);
            j-=2;
        }
        else
        {
            ans.pb(a[i]);
            ans.pb(a[i+1]);
            i+=2;
        }
    }
    ll mul=1;

    for(int i=0;i<k;i++)
    {
        mul*=ans[i];
        mul%=mod;
    }
    if(mul<0)
        cout<<mul+mod<<"\n";
    else
        cout<<mul<<"\n";
 return 0;
}
