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: Time Limit Exceeded)

MOD = 10**9 + 7

N, K = gets.chomp.split.map(&:to_i)
AS = gets.chomp.split.map(&:to_i)

if AS.all? { |a| a <= 0 } && K.odd?
  AS.sort!
  AS.reverse!
  ans = AS[0...K].inject(1, &:*)
  puts ans % MOD 
  exit
end

ans = 1
AS.sort!
AS.reverse!
ans *= AS.shift if K.odd?
(K / 2).times do
  if AS[0] * AS[1] > AS[-1] * AS[-2]
    ans *= AS.shift
    ans *= AS.shift  
  else
    ans *= AS.pop
    ans *= AS.pop
  end
  ans %= MOD
end

puts ans