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)

INF = 10 ** 9 + 7

n, k = gets.chomp.split.map(&:to_i)
a = gets.chomp.split.map(&:to_i)

pos = []
neg = []
a.each do |x|
  if x < 0
    neg << x
  else
    pos << x
  end
end

pos.sort!
neg.sort!

if pos.empty? && k % 2 != 0
  res = 1
  while k > 0
    res *= neg[n - k]
    res %= INF
    k -= 1
  end
  puts res
  exit
end

i = pos.size
j = - 1
k.times do
  if i - 1 < 0
    j += 1 # 負の数を加える
  elsif j + 1 >= neg.size
    i -= 1 # 正の数を加える
  elsif pos[i - 1].abs >= neg[j + 1].abs
    i -= 1
  else
    j += 1
  end
end

if (j + 1) % 2 != 0 && !((i >= pos.size || j >= neg.size - 1) && (j <= -1 || i <= 0))
  if i >= pos.size || j >= neg.size - 1
    i -= 1 # (1)
    j -= 1
  elsif j <= -1 || i <= 0
    j += 1 # (2)
    i += 1
  elsif neg[j] * neg[j - 1] > pos[i] * pos[i + 1]
    i += 1
    j += 1
  else
    i -= 1
    j -= 1
  end
end

res = 1
while i < pos.size
  res *= pos[i]
  res %= INF
  i += 1
end
while j > 0
  res *= (INF + neg[j])
  res %= INF
  j -= 1
end

puts res