Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.

Example 1:

Input: num1 = "2", num2 = "3"
Output: "6"

Example 2:

Input: num1 = "123", num2 = "456"
Output: "56088"

Note:

The length of both num1 and num2 is < 110.
Both num1 and num2 contain only digits 0-9.
Both num1 and num2 do not contain any leading zero, except the number 0 itself.
You must not use any built-in BigInteger library or convert the inputs to integer directly.

The total length the the result should not be longer than len(num1) + len(num2). for num1[i] and num2[j], num1[i] * num2[j] should be stored in i+j and i+j+1 (bigger than 10).
Secondly, travel result array for end to start, if the value is over than 10, than value // 10 should be added to th next value.
Finally, remove the leading zero, except the number 0 itself.

class Solution:
    def multiply(self, num1: str, num2: str) -> str:
        l1, l2 = len(num1), len(num2)
        res = [0 for i in range(l1+l2)]
        for i in range(l1):
            for j in range(l2):
                n1 = num1[l1-1-i]
                n2 = num2[l2-1-j]
                res[l1+l2-i-j-1] += int(n1) * int(n2) % 10
                res[l1+l2-i-j-2] += int(n1) * int(n2) // 10
        # print(res)
        for i in range(l1+l2)[::-1]:
            if res[i] >= 10:
                mul = res[i]
                res[i] = mul % 10
                res[i-1] += mul // 10
        flag = 0
        s = ''
        for i in range(l1+l2-1):
            if flag == 0 and res[i] != 0:
                flag = 1
            if flag == 1:
                s += str(res[i])
        s += str(res[-1])