def make_change(amount, coins)
  @cache = Array.new(amount+1){|i| Array.new(coins.size, i.zero? ? 1 : nil)}
  @coins = coins
  do_count(amount, @coins.length - 1)
end

def do_count(n, m)
  if n < 0 || m < 0
    0
  elsif @cache[n][m]
    @cache[n][m]
  else
    @cache[n][m] = do_count(n-@coins[m], m) + do_count(n, m-1)
  end
end

p make_change(   1_00, [1,5,10,25])
p make_change(1000_00, [1,5,10,25,50,100])