Code Change 2 python3

class Solution:
    def change(self, amount: int, coins: List[int], vals={}) -> int:
        if coins == []:
            return 0

        if vals.get((coins[0], amount)) is not None:
            return vals.get((coins[0], amount))

        multiple = 0
        coin_val = coins[0]
        answer = 1 if amount % coin_val == 0 else 0

        while coin_val * multiple < amount:
            new_amount = amount - (coin_val*multiple)
            answer += self.change(new_amount, coins[1:], vals)
            multiple += 1

        vals[(coin_val, amount)] = answer

        return answer