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: Runtime Error)

n,k = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)
p = []
m = []
for i in 0...n do
  if a[i]>0 then
    p.push(a[i])
  elsif a[i]<0 then
    m.push(a[i])
  end
end

p = p.sort
m = m.sort
    
if p.size+m.size<k then
  puts 0
end

if p.size>=k then
  l = p[0,k]
else
  l = p[0,p.size-p.size%2]
  while l.size<k do
    l.push(m[0])
    m.delete_at(1)
  end
end
ind = p.size-1
while ind-1>=0&&m.size>=2 do
  if l[ind]*l[ind-1] < m[0]*m[1] then
    l[ind] = m[0]
    l[ind-1] = m[1]
    m.delete_at(1)
    m.delete_at(2)
  end
  ind -= 2
end
 
for i in 0...l.size
  ans *= l[i]
end
puts ans