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 int maxn=2e5+100;
const int mod=1e9+7;
const int INF=0x3f3f3f3f;
int A[maxn];
int T,n,m,k;
 
int main()
{
    cin>>n>>k;
    LL res=1,sign=1;
    for(int i=1;i<=n;i++)
        cin>>A[i];
    sort(A+1,A+1+n);
    int l=1,r=n;
    if(k&1)
    {
        res*=A[r--];
        k--;
        if(res<0) sign=-1;
    }
    while(k>0)
    {
        if(1LL*A[l]*A[l+1]*sign>1LL*sign*A[r]*A[r-1])
        {
            res=1LL*A[l]*A[l+1]%mod*res%mod;
            l+=2;
        }
        else
        {
            res=1LL*A[r]*A[r-1]%mod*res%mod;
            r-=2;
        }
        k-=2;
    }
    cout<<(res+mod)%mod<<endl;
}