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.split.map(&:to_i)
AS = gets.split.map(&:to_i)

sorted = AS.sort_by(&:abs).reverse

nums = sorted.first(K)
neg = nums.select { |n| n < 0 }.count

if neg % 2 == 1 && N > K
  ok = false
  sorted[K..-1].each do |n|
    if n > 0
      K.times.each do |i|
        if nums[-i - 1] < 0
          nums[-i - 1] = n
          break
        end
      end
      ok = true
      break
    end
  end
  unless ok
    # 残りは全部マイナス(or zero)の場合
    if neg == nums.count
      # そもそも全部マイナスの場合
      nums = sorted.reject { |n| n == 0 }.last(K)
    else
      # 元の選択に正がある場合
      K.times.each do |i|
        if nums[i] > 0
          nums[i] = sorted[K]
          break
        end
      end
    end
  end
end

result = 1
mod = 10 ** 9 + 7
nums.each do |n|
  result = result * n % mod
end

puts result