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 Julia (1.4.0) (judge verdict: Wrong Answer)

const MOD = 1000000007
function main()
    n, k = parse.(Int, split(readline()))
    a = parse.(Int, split(readline()))
    s = filter(x->x>=0, a)
    t = filter(x->x<0, a)
    sort!(s)
    sort!(t, rev=true)
    S = length(s)
    T = length(t)

    ok = false
    if S > 0
        if n == k
            ok = (T % 2 == 0)
        else
            ok = true
        end
    else
        ok = (k % 2 == 0)
    end

    ans = 1
    if !ok
        sort(a, by=abs)
        for i in 1:k
            ans *= a[i]
            ans = mod(ans, MOD)
        end
    else
        if k%2 == 1
            ans *= pop!(s)
        end
        p = Int[]
        while length(s) >= 2
            x = pop!(s)
            x *= pop!(s)
            push!(p, x)
        end
        while length(t) >= 2
            x = pop!(t)
            x *= pop!(t)
            push!(p, x)
        end
        sort!(p, rev=true)
        for i in 1:k÷2
            ans *= mod(p[i], MOD)
            ans = mod(ans, MOD)
        end
    end
    println(ans)
end

main()