Problem:
Score: 400 points

Problem Statement

We have N integers A_1, A_2, ..., A_N.

There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?

Constraints

All values in input are integers.

2 \leq N \leq 2 \times 10^5

1 \leq K \leq \frac{N(N-1)}{2}

-10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \dots A_N

Output

Print the answer.

Sample Input 1

4 3
3 3 -4 -2

Sample Output 1

-6

There are six ways to form a pair. The products of those pairs are 9, -12, -6, -12, -6, 8.

Sorting those numbers in ascending order, we have -12, -12, -6, -6, 8, 9. The third number in this list is -6.

Sample Input 2

10 40
5 4 3 2 -1 0 0 0 0 0

Sample Output 2

6

Sample Input 3

30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0

Sample Output 3

448283280358331064

Solution in Julia (0.5.0) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env -S JULIA_VERSION=0.5.0 julia
# contest: abc155, problem: abc155_d, alphabet: D

function cnt(x, P, M)
  ans = 0
  for p in reverse(P)
    ans += searchsortedlast(M .* p, x)
  end
  x < 0 && return ans

  for (pi, p) in enumerate(P)
    ans += searchsortedlast(@view(P[pi+1:end]) .* p, x)
  end
  revM = reverse(M)
  for (mi, m) in enumerate(revM)
    ans += searchsortedlast(@view(revM[mi+1:end]) .* m, x)
  end
  ans
end

function solve(N::Int, K::Int, A::Vector{Int})
  P = [x for x in A if x >= 0]
  M = [x for x in A if x < 0]
  sort!(P)
  sort!(M)

  bottom = -10^18 - 100
  top = 10^18 + 100
  while bottom < top
    mid = div(top + bottom, 2)
    cmid = cnt(mid, P, M)
    if bottom == top - 1
      println(top)
      return
    elseif cmid < K
      bottom = mid
    else
      top = mid
    end
  end
end

function main()
  tokens = Channel{String}(32)
  Task() do
    for line in eachline(@static VERSION < v"0.6" ? STDIN : stdin)
      startswith(line, '\0') && break
      for token in split(chomp(line))
        put!(tokens, token)
      end
    end
    close(tokens)
  end |> schedule
  N = parse(Int, take!(tokens))
  K = parse(Int, take!(tokens))
  A = similar(Vector{Int}, N)
  for i in 1:N
    A[i] = parse(Int, take!(tokens))
  end
  solve(N, K, A)
end

if isempty(get(ENV, "ATCODER_LOCAL", ""))
  isempty(ARGS) && main()
else
  @eval begin
    const samples = [("4 3\n3 3 -4 -2", "-6"), ("10 40\n5 4 3 2 -1 0 0 0 0 0", "6"), ("30 413\n-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0", "448283280358331064")]
    function test(sampleids...)
      isempty(sampleids) && return test(collect(1:length(samples))...)
      ostdin, ostdout = @static VERSION < v"0.6" ? (STDIN, STDOUT) : (stdin, stdout)
      rd, wr = first(redirect_stdout()), last(redirect_stdin())
      try
        map(sampleids) do sampleid
          input, output = samples[sampleid]
          print(ostdout, "Testing sample #$(sampleid)..."); flush(ostdout)
          println(wr, input)
          println(wr, "\0")
          t = @elapsed main()
          println()
          result = strip(String(readavailable(rd)))
          if result == output
            println(ostdout, "OK ($t sec).")
            true
          else
            println(ostdout, "ERROR ($t sec)")
            println(ostdout, "== expected ==\n$output")
            println(ostdout, "== actual ==\n$result\n")
            false
          end
        end |> all
      finally
        redirect_stdin(ostdin)
        redirect_stdout(ostdout)
      end
    end
    submit() = test() && (prog = @__FILE__; run(`atcoder-submit $prog`))
    !isinteractive() && submit()
  end
end