Can I Win Python Solution with Tests

lcpy gen -n 464   # by problem number
lcpy gen -s can_i_win   # by problem name

Input: maxChoosableInteger = 10, desiredTotal = 11
Output: false
Explanation:
No matter which integer the first player choose, the first player will lose.
The first player can choose an integer from 1 up to 10.
If the first player choose 1, the second player can only choose integers from 2 up to 10.
The second player will win by choosing 10 and get a total = 11, which is >= desiredTotal.
Same with other integers chosen by the first player, the second player will always win.

Input: maxChoosableInteger = 10, desiredTotal = 0
Output: true

Input: maxChoosableInteger = 10, desiredTotal = 1
Output: true

class Solution:
    # Time: O(2^m * m) where m = max_choosable_integer
    # Space: O(2^m)
    def can_i_win(self, max_choosable_integer: int, desired_total: int) -> bool:
        if desired_total <= 0:
            return True
        pool = max_choosable_integer * (max_choosable_integer + 1) // 2
        if pool < desired_total:
            return False

        memo: dict[int, bool] = {}

        def dfs(used: int, remaining: int) -> bool:
            if used in memo:
                return memo[used]
            for choice in range(max_choosable_integer):
                bit = 1 << choice
                if used & bit:
                    continue
                if choice + 1 >= remaining or not dfs(used | bit, remaining - choice - 1):
                    memo[used] = True
                    return True
            memo[used] = False
            return False

        return dfs(0, desired_total)