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;
typedef long long ll;
const ll mod=1e9+7;
ll A[300001];
int main()
{
    ll n,k;
    cin>>n>>k;

    for(int i=0; i<n; i++)
        cin>>A[i];
    sort(A,A+n);
    ll ans=1,sign=0;
    int l=0,r=n-1;
    if(k%2)
    {
        ans=A[r];
        r--;
        --k;
        if(ans<0)
            sign=1;
    }
    while(k)
    {
        ll x=A[l]*A[l+1],y=A[r]*A[r-1];
        if(sign)
        {
            if(x>=y)
            {
                ans=y%mod*ans%mod;
                r-=2;
            }
            else
            {
                ans=x%mod*ans%mod;
                l+=2;
            }
        }
        else
        {
            if(x<=y)
            {
                ans=y%mod*ans%mod;
                r-=2;
            }
            else
            {
                ans=x%mod*ans%mod;
                l+=2;
            }
        }
        k-=2;
    }
    cout<<(ans+mod)%mod<<endl;
    return 0;
}
