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)

require 'pp'

def puts_answer(ans)
    o = 1
    ans.each do |t|
        o = (o * t) % MOD
    end

    o
end

MOD = 10 ** 9 + 7
n, k = gets.split.map(&:to_i)
a_n = gets.split.map(&:to_i)

# 全選択するしかない
if a_n.length == k
    ans = a_n
    puts puts_answer(ans)
    exit 0
end

# 0 を除く
len = a_n.length
a_n.delete_if {|a| a == 0}
is_zero = (len != a_n.length) 
# pp is_zero
# 0を答えに含むしかないので答えは0
if a_n.length < k
    puts 0
    exit 0
end

minus = []
plus = []

a_n.each do |a|
    if a > 0
        plus << a
    else
        minus << a
    end
end

plus.sort!.reverse!
minus.sort!

ans = []

if k % 2 != 0
    # 選択する個数が奇数

    # 最初の一つは必ず正の一番でかい数をとる
    # ただし正の数をとれない場合は負数しかないので，答えは負なので絶対値が一番小さくなるようにする
    x = plus.shift
    if x == nil
        if is_zero
            puts 0
            exit 0
        else
            ans = minus.reverse![0, k]
            puts puts_answer(ans)
            exit 0
        end
    end

    ans << x
    k = k - 1
end

# これで残りはkが偶数
pp plus
pp minus
z = false
while k != 0
    x, b = 
        if plus.length == 1 && minus.length == 1
            [minus[0] * plus[0], :xxx]
        elsif plus[0] == nil || plus[1] == nil
            [minus[0] * minus[1], :minus]
        elsif minus[0] == nil || minus[1] == nil
            [plus[0] * plus[1], :plus]
        else
            p1 = plus[0] * plus[1]
            m1 = minus[0] * minus[1]
            if p1 >= m1
                [p1, :plus]
            else
                [m1, :minus]
            end
        end

    if b == :plus
        ans << plus.shift
        ans << plus.shift
    elsif b == :minus
        ans << minus.shift
        ans << minus.shift
    else
        ans << minus.shift
        ans << plus.shift
        z = true
    end

    k -= 2
end

if z && is_zero
    puts 0
else
    puts puts_answer(ans)
end