print all paths which sum to a given value

def find_tree_sum(start, sum)
  $last_sum ||= 0
  $result ||= []

  if start.nil?
    return false
  end

  $last_sum += start.value
  $result << start.value

  

  if $last_sum == sum
    return $result
  elsif $last_sum > sum
    value = $result.delete_at($result.length - 1)
    $last_sum -= value if value
  elsif $last_sum < sum
    if start.left.nil? && start.right.nil?
      value = $result.delete_at($result.length - 1)
      $last_sum -= value if value
      return false
    end
  end

  if start.left && find_tree_sum(start.left, sum)
    return $result
  end

  if start.right && find_tree_sum(start.right, sum)
    return $result
  end

  false
end