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: Wrong Answer)

n, k = gets.chomp.split.map(&:to_i)
a = gets.chomp.split.map(&:to_i).sort_by { |e| e.abs }.reverse

horyu = 0
used_count = 0
res = 1
a.each do |e|
  if used_count >= k
    break
  end

  if used_count == k - 1 && horyu != 0
    horyu = 0
  end

  if e < 0
    if horyu == 0
      horyu = e
    else
      res *= horyu
      res *= e
      horyu = 0
      used_count += 2
    end
  else
    res *= e
    used_count += 1
  end
end

if used_count != k
  res = a[a.size - k, k].inject(:*)
end

p res % 1000000007