1815. Maximum Number of Groups Getting Fresh Donuts

class Solution:
    def maxHappyGroups(self, batchSize: int, groups: List[int]) -> int:
        @cache
        def dfs(state, x):
            if state == mask:
                return 0
            vis = [False] * batchSize
            res = 0
            for i, v in enumerate(g):
                if state >> i & 1 == 0 and not vis[v]:
                    vis[v] = True
                    y = (x + v) % batchSize
                    res = max(res, dfs(state | 1 << i, y))
            return res + (x == 0)

        g = [v % batchSize for v in groups if v % batchSize]
        mask = (1 << len(g)) - 1
        return len(groups) - len(g) + dfs(0, 0)