merge sort ruby - the ruby way?

gistfile1.txt

def merge_sort(m)
  #base case
  if m.length <= 1
    m
  #all other cases
  else
    #intialize variables
    left = Array.new
    right = Array.new
    middle = m.length/2

    #split first half to left and second half to right, call merge sort recursively
    left = merge_sort(m[0..middle-1])
    right = merge_sort(m[middle..-1])

    #merge left and right
    merge = merge(left, right)
    
    #return merge
    merge
  end
end

def merge(left, right)
  #initializations
  output = Array.new(left.length+right.length)
  i = 0
  j = 0

  #go through each element in the ouput array and insert a value from left or right
  output.each_with_index do |k, index|
    #before the counters for either left and right have ended    
    if i < left.length && j < right.length  
      if left[i] < right[j]
        output[index]=left[i]
        i += 1
      else
        output[index]=right[j]
        j += 1
      end
    #when counter for left has reached end, but right has not
    elsif i >= left.length && j < right.length
        output[index]=right[j]
        j += 1
    #when counter for right has reached end, but left has not
    elsif i < left.length && j >= right.length
        output[index]=left[i]
        i += 1    
    end
  end
  
  #return ouput
  output
end