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)

n,k = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)
MOD = 10**9+7
a = a.sort_by{|x| x.abs}.reverse
aa = a.clone
aa.sort!
aaa = 1
for i in 0..(k-1)
  if a[i] < 0
    aaa *= -1
  elsif a[i] == 0
    aaa = 0
  end
end
d = Array.new(4)
0.upto(k-1) do |j|
  if a[j] > 0
    d[0] = a[j].abs
  elsif a[j] < 0
    d[1] = a[j].abs
  end
end
(n-1).downto(k) do |l|
  if a[l] > 0
    d[2] = a[l].abs
  elsif a[l] < 0
    d[3] = a[l].abs
  end
end


if aa[-1] < 0 && k%2==1
  puts a.reverse.slice(0..(k-1)).inject{|x,y| x = (x*(y%MOD))%MOD}
  exit
end

require 'openssl'

if n == k
  puts a.inject{|x,y| x = (x*(y%MOD))%MOD}
else
  if aaa > 0
    puts a.slice(0..(k-1)).inject{|x,y| x = (x*(y%MOD))%MOD}
  elsif aaa == 0
    puts 0
  else
    if a[k] == 0
      puts 0
    elsif ((d[3].to_f)/(d[0].to_f)) >= ((d[2].to_f)/(d[1].to_f))
      puts a.slice(0..(k-1)).inject{|x,y| x = (x*(y%MOD))%MOD} * (d[3]%MOD) * d[0].to_bn.mod_inverse(MOD).to_i * -1 % MOD
    else
      puts a.slice(0..(k-1)).inject{|x,y| x = (x*(y%MOD))%MOD} * (d[2]%MOD) * d[1].to_bn.mod_inverse(MOD).to_i * -1 % MOD
    end
  end
end