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: Wrong Answer)

MOD = 10 ** 9 + 7
N, K = gets.split.map(&:to_i)
A = gets.split.map(&:to_i).sort
neg_cnt = A.count { |n| n < 0 }
has_zero = A.any? { |n| n == 0 }

ans = 1
if K % 2 == 1 && neg_cnt == N
  if has_zero
    ans = 0
  else
    A.sort! { |a, b| a.abs <=> b.abs }
    A[0, K].each do |n|
      ans *= n
      ans %= MOD
    end
  end
else
  minus_idx = 0
  plus_idx = N-1
  K.times do
    if A[minus_idx] <= 0 && A[minus_idx].abs > A[plus_idx]
      ans *= A[minus_idx]
      ans %= MOD
      minus_idx += 1
    else
      ans *= A[plus_idx]
      ans %= MOD
      plus_idx -= 1
    end
  end
  if N != K && minus_idx % 2 == 1
    ans += MOD
    ans /= A[minus_idx-1]
    ans *= A[plus_idx]
    ans %= MOD
  end
end

puts(ans)