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)

mod=1000000007
n,k=gets.split.map(&:to_i)
a=gets.split.map(&:to_i)
pl=[]
mn=[]
zr=[]
a.each do |aa|
  if aa>0
    pl << aa
  elsif aa<0
    mn << aa
  else
    zr << aa
  end
end
pl.sort!.reverse!
mn.sort!
ni=pl.size
nj=mn.size
i=0
j=0
c=1
if nj==n
  if k.odd?
    mn.reverse!
    k.times do |jj|
      c=c*mn[jj]%mod
    end
    puts c
    exit
  else
    k.times do |jj|
      c=c*mn[jj]%mod
    end
    puts c
    exit
  end
end
if n==k
  a.each do |aa|
    c=c*aa%mod
  end
  puts c
  exit
end
while k>0
  if k==1||j>=nj-1
    if i<ni
      c=c*pl[i]%mod
      k-=1
      i+=1
    else
      c=0
      k-=1
    end
  elsif i<ni-1
    if pl[i]*pl[i+1]<mn[j]*mn[j+1]
      c=c*mn[j]*mn[j+1]%mod
      k-=2
      j+=2
    else
      c=c*pl[i]%mod
      k-=1
      i+=1
    end
  else
    c=c*mn[j]*mn[j+1]%mod
    k-=2
    j+=2
  end
end
puts c