Minimum XOR Sum of Two Arrays LeetCode solution in Python

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class Solution:
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    def minimumXORSum(self, a: List[int], b: List[int]) -> int:
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        @cache
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        def dp(mask: int) -> int:
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            i = bin(mask).count("1")
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            if i >= len(a):
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                return 0
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            return min(
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                (a[i] ^ b[j]) + dp(mask + (1 << j))
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                for j in range(len(b))
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                if mask & (1 << j) == 0
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            )
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        return dp(0)