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;
int mod=1e9+7;
const int N=2e5+100;
ll a[N];
int f[5];
bool cmp(int x,int y)
{
    return abs(x)<abs(y);
}
int main()
{
    ios::sync_with_stdio(0);cin.tie(0);
    int n,m;
    cin>>n>>m;
    for(int i=1;i<=n;i++) {
        cin>>a[i];
        if(a[i]>=0) f[1]++;
        else f[2]++;
    }
    int l=1,r=n;
    ll ans=1;
     if(!f[1]&&m%2==1){
        sort(a+1,a+1+n,cmp);
        for(int i=1;i<=m;i++){
            ans=a[i]*ans%mod;
        }
    }
    else {
        sort(a+1,a+1+n,greater<int>());
    while(m>0){
        if(m%2) ans=ans*a[l]%mod,l++,m--;
        else if(m>=2){
           if(a[l]*a[l+1]>=a[r]*a[r-1]){
              ans=ans*a[l]%mod*a[l+1]%mod;
              l+=2;
              m-=2;
           }
           else{
            ans=ans*a[r-1]%mod*a[r]%mod;
            r-=2;
            m-=2;
           }
        }
    }
    }
    cout<<(ans%mod+mod)%mod<<endl;
    return 0;
}

