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)

def gs() gets.chomp end
def gi() gets.to_i end
def gsmi() gets.chomp.split.map(&:to_i) end

def desc(ar) ar.sort!{|x,y|y<=>x} end
def min(a,b) a<=b ? a : b end
def max(a,b) a>=b ? a : b end
def sum(ar) ar.inject(:+) end
def mult(ar) ar.inject(:*) end

n, k = gsmi #10**5
as = gsmi #10**9
mod = 10**9 + 7

ses = []
fus = []
zeros = []
as.each do |a|
  if a>0
    ses << a
  elsif a==0
    zeros << 0
  else
    fus << a
  end
end

ses.sort! # [0,1,2,3]
desc fus # [-1,-2,-3]

ans = 1
seifu = true

if (k-ses.size-fus.size)>0
  puts 0
  exit
end

if ses.empty?
  if k.odd?
    ans = mult(fus[0...k]) % mod
  else
    ans = mult(fus[(-1*k)..-1]) % mod
  end
elsif fus.empty?
  ans = mult(ses[(-1*k)..-1]) % mod
else
  k.times do |i|
    if fus.size==1
      p "1"
      mul = fus.pop if !seifu||ses.empty?
      mul = ses.pop if seifu&&!ses.empty?
    elsif ses.size==1
      p "2"
      if ((k-i).odd?&&seifu) || (!(k-i).odd?&&!seifu)
        mul = ses.pop
      else
        mul = fus.pop
        seifu = !seifu
      end
    else
      p "3"
      if i==(k-1)
        if seifu
          mul = ses.pop
        else
          mul = fus.pop
          seifu = !seifu
        end
      else
        if ses[-1]>fus[-1].abs
          mul = ses.pop
        else
          mul = fus.pop
          seifu = !seifu
        end
      end
    end
    p mul
    ans *= (mul) % mod
    ans %= mod
  end
end

puts ans