Minimum Operations to Convert Number — C++

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

class Solution {
public:
    int minimumOperations(vector<int>& nums, int start, int goal) {
        static const int MAX_X = 1000;

        vector<int> new_nums;
        for (const auto& y : nums) {
            if (y && ((0 <= y && y <= MAX_X) || (0 <= (goal - y) && (goal - y) <= MAX_X) || (0 <= (goal + y) && (goal + y) <= MAX_X) || (0 <= (goal ^ y) && (goal ^ y) <= MAX_X))) {
                new_nums.emplace_back(y);
            }
        }
        nums = move(new_nums);
        vector<pair<int, int>> q = {{start, 0}};
        unordered_set<int> lookup = {start};
        while (!empty(q)) {
            vector<pair<int, int>> new_q;
            for (const auto& [x, steps] : q) {
                for (const auto& y : nums) {
                    for (const auto& nx : {x + y, x - y, x ^ y}) {
                        if (nx == goal) {
                            return steps + 1;
                        }
                        if (!(0 <= nx && nx <= MAX_X) || lookup.count(nx)) {
                            continue;
                        }
                        lookup.emplace(nx);
                        new_q.emplace_back(nx, steps + 1);
                    }
                }
            }
            q = move(new_q);
        }
        return -1;
    }
};