def addOperators(self, num, target):
        """
        Adapted from https://leetcode.com/discuss/58614/java-standard-backtrace-ac-solutoin-short-and-clear

        Algorithm:
        1. DFS
        2. Special handling for multiplication
        3. Detect invalid number with leading 0's
        :type num: str
        :type target: int
        :rtype: List[str]
        """
        ret = []
        self.dfs(num, target, 0, "", 0, 0, ret)
        return ret