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)

M=10**9+7
N,K=gets.split.map(&:to_i)
A=gets.split.map(&:to_i).sort{|l,r|l.abs<=>r.abs}
PLS=A.select{|a|0<=a}.sort{|l,r|r<=>l}
MNS=A.select{|a|a<0}.sort

def calc(n)
  m=K-n
  exit(1) if m<0
  exit(1) if PLS.size<m
  MNS[0...n].inject(1){|s,a|s*a%M} * PLS[0...m].inject(1){|s,a|s*a%M} % M
end

def odd(n)
  m=K-n
  return 0 if calc(n).zero?
  return calc(n-1) if n==MNS.size
  return calc(n+1) if m==PLS.size
  return calc(n+1) if m.zero?
  x=Rational(PLS[m].abs, MNS[n-1].abs)
  y=Rational(MNS[n].abs, PLS[m-1].abs)
  x<y ? calc(n+1) : calc(n-1)
end

if K.odd? && PLS.empty?
  s=A[0...K].inject(1){|s,a|s*a%M}
  s+=M
  p s%M
  exit
end

n=A[-K..-1].count{|a|a<0}
p n.even? ? calc(n) : odd(n)