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: Runtime Error)

m = 10 ** 9 + 7

n, k = gets.split.map(&:to_i)
a = gets.split.map(&:to_i).sort!

if k == n
    ans = a.inject(1) {|r,v| r * v % m}
elsif a[-1] <= 0 && k.odd?
    a.reverse!
    ans = a[0, k].inject{|r,v| r * v % m}
elsif a[0] >= 0
    a.reverse!
    ans = a[0, k].inject{|r,v| r * v % m}
else
    x = a.index{|e| e >= 0}

    s = a[0..x-1]
    t = a[x..-1]

    ans = 1
    while k > 0
        if s.size < 2 
            k.times {ans = ans * t.pop % m}
            break
        elsif t.size < 2
            if k > 1
                ans = ans * s.shift * s.shift % m
                k -= 2
            else
                ans = ans * t.pop % m
                break
            end
        else
            x = s[0] * s[1]
            y = t[-1] * t[-2]
            if x > y
                ans = ans * s.shift * s.shift % m
            else
                ans = ans * t.pop * t.pop % m
            end
            k -= 2
        end
    end
end

puts ans