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)

s = []
t = []
z = false
gets.split.each do |e|
    e = e.to_i
    e == 0 ? z = true : e < 0 ? s << e : t << e
end

s.sort!
t.sort!

x = k - t.size
x = x + x[0] < k ? x + x[0] : k
ans = 1
if x.even? && x <= s.size
    s.reverse!
    while k > 0
        if s.empty? || (t.size == 1 && k.odd?)
            ans = ans * t.pop % m
        elsif t.empty?
            ans = ans * s.pop % m
        else
            x = s[-1] * s[-2]
            y = t[-1] * t[-2]
            if x > y
                ans = ans * x % m
                s.pop
                s.pop
            else
                ans = ans * y % m
                t.pop
                t.pop
            end
            k -= 1
        end
        k -= 1
    end
elsif z
    ans = 0
else
    t.reverse!
    while k > 0
        if s.empty?
            ans = ans * t.pop % m
        elsif t.empty?
            ans = ans * s.pop % m
        else
            x = s[-1].abs
            y = t[-1].abs
            if x < y
                ans = ans * s.pop % m
            else
                ans = ans * t.pop % m
            end
        end
        k -= 1
    end
end

puts ans