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)
a    = gets.split.map!(&:to_i).sort!
@m = 10**9 + 7

i1 = a.bsearch_index { |x| x >= 0 } || n
i2 = a.bsearch_index { |x| x >  0 } || n

an = a[0...i1]
ap = a[i2..-1].reverse!
nz = i2 - i1

if k > n - nz
  puts 0
  exit
end

if ap.empty? && k.odd?
  if nz > 0
    puts 0
  else
    puts an.reverse.take(k).inject(1) { |prod, x| prod * x % @m }
  end
  exit
end

init = k.odd? ? ap.shift : 1
k /= 2
ap = ap.each_slice(2).map { |x, y| x * (y || 1) }
an = an.each_slice(2).map { |x, y| x * (y || 1) }
a2 = (ap + an).sort!.reverse!
puts a2.take(k).inject(init) { |prod, x2| prod * x2 % @m }