class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> res;
        res.push_back(0);

        long pow2 = 1;
        for (int i=1; i <= n; i++) {
            int old_len = res.size();
            for (int i=0; i<old_len; i++) {
                res.push_back(pow2 + res[old_len - i - 1]);
            }
            pow2<<=1;
        }
        return res;
    }   
};