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,*as=$<.read.split.map(&:to_i)
# N,K,*as = [4, 3, -3,-2,-1,0]
MOD = 10**9+7

def mult(as)
    n = 1
    as.each do |a|
        n = n * a % MOD
    end
    n
end

as.sort_by! {|a| -(a.abs)}
ls = as[0...K]
rs = as[K..-1]
mul = mult(ls)
if ls[-1] == 0 || ls.count {|a| a < 0}.even?
    puts mul
    exit
end


if li = ls.rindex{|a| 0 < a} && ri = rs.index{|a| a < 0}
    puts (mul / ls[li] * rs[ri]) % MOD
elsif li = ls.rindex{|a| a < 0} && ri = rs.index{|a| 0 < a}
    puts (mul / ls[li] * rs[ri]) % MOD
elsif as.include?(0)
    puts 0
else
    puts mult(as[-K..-1])
end