### addOperators 
from typing import *
def f_gold(num: str, target: int) -> List[str]:
    ans = []
    def dfs(u, prev, curr, path):
        if u == len(num):
            if curr == target:
                ans.append(path)
            return
        for i in range(u, len(num)):
            if i != u and num[u] == '0':
                break
            next = int(num[u : i + 1])
            if u == 0:
                dfs(i + 1, next, next, path + str(next))
            else:
                dfs(i + 1, next, curr + next, path + "+" + str(next))
                dfs(i + 1, -next, curr - next, path + "-" + str(next))
                dfs(
                    i + 1,
                    prev * next,
                    curr - prev + prev * next,
                    path + "*" + str(next),
                )
    dfs(0, 0, 0, "")
    return ans