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 Ruby (2.7.1) (judge verdict: Accepted)

MOD=10**9+7
n, k=gets.split.map &:to_i
a=gets.split.map(&:to_i).sort_by(&:abs).reverse

res=1
nc=0
neg=[]
pos=[]
(0...k).each{|i|
    res=res*a[i].abs%MOD
    if a[i]<0
        neg << a[i].abs
        nc+=1
    else
        pos << a[i]
    end
}

if nc.even? || n==k
    res=-res%MOD if nc.odd?
    puts res
    exit
end

x, y=a[k...n].minmax

if x>=0
    res=res*neg[-1].pow(MOD-2, MOD)*y%MOD
    puts res
    exit
end

if y<=0
    if pos.size>0
        res=res*pos[-1].pow(MOD-2, MOD)*x.abs%MOD
    else
        res=1
        (1..k).each{|i| res=res*a[-i].abs%MOD }
        res=-res%MOD
    end
    puts res
    exit
end

if pos.size>0 && neg[-1]*x.abs>pos[-1]*y
    res=res*pos[-1].pow(MOD-2, MOD)*-x%MOD
else
    res=res*neg[-1].pow(MOD-2, MOD)*y%MOD
end
puts res