defmodule MaxCounters do
  def max_counters(n, a) do
    condition = n + 1

    {counters, _max_counter, last_update} =
      Enum.reduce(a, {%{}, 0, 0}, fn v, {counters, max_counter, last_update} ->
        cond do
          v <= n ->
            index = v - 1
            updated = max(Map.get(counters, index, 0), last_update) + 1
            {Map.put(counters, index, updated), max(max_counter, updated), last_update}

          v == condition ->
            {counters, max_counter, max_counter}

          true ->
            {counters, max_counter, last_update}
        end
      end)

    0..(n - 1)
    |> Enum.map(fn i -> max(Map.get(counters, i, 0), last_update) end)
  end
end