class Solution {
public:
    string add(string num1, string num2) {
        int end1 = num1.size()-1;
        int end2 = num2.size()-1;
        int next = 0;
        int val1 = 0;
        int val2 = 0;
        string ret;
        while(end1>=0 || end2 >= 0)
        {
            if(end1 >= 0)
            {
                val1 = num1[end1--]-'0';
            }
            else
            {
                val1 = 0;
            }
            if(end2 >= 0)
            {
                val2 = num2[end2--]-'0';
            }
            else
            {
                val2 = 0;
            }
            int valRet = val1+val2+next;
            if(valRet>9)
            {
                next = 1;
            }
            else
            {
                next = 0;
            }
            ret += (valRet%10+'0');
        }
        if(next == 1)
        {
            ret += '1';
        }
        reverse(ret.begin(),ret.end());
        return ret;
    }
    string multi(string num1,char num){
        string ans="0";
        int n2=num-'0';
        int j=0;
        for(int i=num1.size()-1;i>=0;--i)
        {
            int n1=num1[i]-'0';
            int temp=n1*n2;
            string temps=to_string(temp);
            for(int z=0;z<j;++z)
            {
                temps.push_back('0');
            }
            ans=add(ans,temps);
            ++j;
        }
        return ans;
} 
    string multiply(string num1, string num2) {
        string ans;
        int j=0;
        if(num1=="0"||num2=="0")
        return "0";
        for(int i=num1.size()-1;i>=0;--i)
        {
            string temp=multi(num2, num1[i]);
            for(int z=0;z<j;++z)
            {
                temp.push_back('0');
            }
            ++j;
            ans=add(ans, temp);
        }
        return ans;     
    }
};