Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in Python (3.8.2) (judge verdict: Wrong Answer)

n,k=map(int,input().split())
A=[int(i) for i in input().split()]
A.sort(key=lambda x:-abs(x))
mod=10**9+7

ans=1
if max(A)<=0 or n==k:
    for i in range(k):
        ans=ans*A[n-1-i]%mod
else:
    mi=0
    pl=0
    flg=1
    for i in range(k):
        ans=ans*A[i]%mod
        if A[i]>0:
            pl=A[i]
        if A[i]<0:
            mi=A[i]
            flg*=-1
    if ans==0:
        pass
    elif flg==-1:
        mi2=None
        pl2=None
        for i in range(k,n):
            if A[i]>=0:
                pl2=A[i]
                break
        for i in range(k,n):
            if A[i]<=0:
                mi2=A[i]
                break
        can=0
        if mi!=0 and pl2 is not None and pl!=0 and mi2 is not None:
            if pl2*pl > mi2*mi:
                can = pow(mi,-1,mod)*pl2%mod
            else:
                can = pow(pl,-1,mod)*mi2%mod
        elif mi!=0 and pl2 is not None:
            can = pow(mi,-1,mod)*pl2%mod
        elif pl!=0 and mi2 is not None:
            can = pow(pl,-1,mod)*mi2%mod 
        ans=ans*can%mod

print(ans)