class Solution {

public:

    string multiply(string num1, string num2) {

        if(num1.empty() || num1.size() ==  || num2.empty() || num2.size() == )

            return "";

        //

        if(num1 == "" || num2 == "")

            return "";

        //keep num2 the smaller

        if(num1.size() < num2.size())

        {

            //exchange

            string t = num1; num1 = num2; num2 = t;

        }

        string ans = "";

        ans.resize(num1.size());

        //initialize

        for(size_t i = ; i < num1.size(); i++)

            ans[i] = '';

        int pos = ;

        int times = ;

        int sum = ;

        for(int index2 = num2.size() - ; index2 >= ; index2--)

        {

            pos = ans.size() -  - times;

            times++;

            int carry = ;

            for(int index1 = num1.size() - ; index1 >=; index1--)

            {

                sum = carry + (num1[index1] - '')*(num2[index2] - '') + ans[pos] - '';

                carry = sum/;

                ans[pos] = sum% + '';

                pos--;

                // ans has been the beginning while index1 not, and ans has been the beginning and here are carry

                if(pos == - &&(carry > || index1 != ))

                {

                    string t = "";

                    t[] = carry + '';

                    ans = t + ans;

                    carry = ;

                    pos = ;

                }

            }

        }

        return ans;

    }

};