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>
#define ll long long
#define FAST {ios_base::sync_with_stdio(false);cin.tie(NULL);}
#define f(i, a, b) for(ll i=a; i<b; i++)
#define fr(i,a,b) for(ll i=a;i>=b;i--)
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define pll pair<ll,ll>
#define LB lower_bound
#define UB upper_bound
#define endl "\n"
using namespace std;

ll M=1e9+7;
int main()
{
    FAST
    ll n,k;cin>>n>>k;
    ll a[n];f(i,0,n) cin>>a[i];
    sort(a,a+n);
    ll l=0,r=n-k;
    while(l<r && r+1<=n-1)
    {
        if(a[l]*a[l+1]>=a[r]*a[r+1]) l+=2,r+=2;
        else break;
    }
    ll ans=1;
    if(a[n-1]<0 && k&1LL) l=0,r=n-k;
    f(i,0,l) ans=(ans*a[i])%M;
    f(i,r,n) ans=(ans*a[i])%M;
    ans=(ans+M)%M;
    cout<<ans<<endl;
}
