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)

#input of int(split by space)
def get_i()
  return gets.chomp.split(" ").map(&:to_i)
end
#input of float(split by space)
def get_f()
  return gets.chomp.split(" ").map(&:to_f)
end
#input of string(split by space)
def get()
  return gets.chomp.split(" ")
end
#input of string(split per one character)
def get_nsp()
  return gets.chomp.split("")
end
#yes or no decision
def yn_judge(bool,y="Yes",n="No")
  return bool ? y : n 
end
#create of array
def array(size1,init=nil,size2=-1)
  if size2==-1
      return Array.new(size1){init}
  else
      return Array.new(size2){Array.new(size1){init}}
  end
end

def max(a,b)
    return a>b ? a : b
end

def min(a,b)
    return a>b ? b : a
end

INF=Float::INFINITY

N,K=get_i
#N=10**5+1
#K=N
#A=(0..N+5).to_a.sort{|x,y| y<=>x}
MOD=10**9+7
A=get_i.sort!{|x,y| y.abs<=>x.abs}
accum=array(N+1,0)
N.times do|i|
  accum[i+1]=accum[i]+(A[i]<0 ? 1 : 0)
end
if accum[K].even?
    ans=1
    K.times do|i|
      ans*=A[i].abs
      ans%=MOD
    end
    puts ans
else
    if accum[N]==N
        #puts A[N-K..N-1].inject(:*)%MOD
        ans=1
        (N-K).upto(K-1) do|i|
          ans*=A[i].abs
          ans%=MOD
        end
        puts (MOD-ans)%MOD
        exit
    end
    flag=false
    ans=1
    (K-1).downto(0) do|i|
        if not flag and A[i]<0
            flag=true
        else
            ans*=A[i]
            ans%=MOD
        end
    end
    K.upto(N-1) do|i|
        if A[i]>0
            ans*=A[i]
            ans%=MOD
            break
        end
    end
    puts ans
end