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: Accepted)

C = 10 ** 9 + 7

def modinv(a, m)
  b, u, v = m, 1, 0
  until b.zero?
    t = a / b
    a -= t * b
    a, b = b, a
    u -= t * v
    u, v = v, u
  end
  u %= m
  u += m if u < 0
  u
end

n, k = gets.split.map(&:to_i)
seq = gets.split.map(&:to_i).sort_by {-_1.abs}

tmp = seq[0, k]
f0 = seq.all? {_1 < 0}
f1 = tmp.map {_1 <=> 0}.inject(:*)
ans = tmp.inject(1) {|acc, i| acc * i % C}

ans = if k == n || f1 >= 0
  ans
elsif f0 && k.odd?
  seq[n - k, k].inject(1) {|acc, i| acc * i % C}
else
  x1 = x2 = y1 = y2 = nil
  tmp.reverse_each do |i|
    if i < 0
      x1 = i
      break
    end
  end
  tmp.reverse_each do |i|
    if i > 0
      x2 = i
      break
    end
  end
  seq[k..].each do |i|
    if i >= 0
      y1 = i
      break
    end
  end
  seq[k..].each do |i|
    if i < 0
      y2 = i
      break
    end
  end
  
  if !x2 || !y2
    ans * y1 * modinv(x1, C) % C
  elsif !x1 || !y1
    ans * y2 * modinv(x2, C) % C
  elsif (x2 * y1).abs > (x1 * y2).abs
    ans * y1 * modinv(x1, C) % C
  else
    ans * y2 * modinv(x2, C) % C
  end 
end

puts ans