# Time:  O(n * m), m is max x
# Space: O(m)

class Solution(object):
    def minimumOperations(self, nums, start, goal):
        """
        :type nums: List[int]
        :type start: int
        :type goal: int
        :rtype: int
        """
        MAX_X = 1000
        nums = [y for y in nums if y and any(0 <= nx <= MAX_X for nx in (y, goal-y, goal+y, goal^y))]
        q = [(start, 0)]
        lookup = {start}
        while q:
            new_q = []
            for x, steps in q:
                for y in nums:
                    for nx in (x+y, x-y, x^y):
                        if nx == goal:
                            return steps+1
                        if not (0 <= nx <= MAX_X) or nx in lookup:
                            continue
                        lookup.add(nx)
                        q.append((nx, steps+1))
            q = new_q
        return -1