class Solution {
public:
    string mul(string a, int p){
        int cnt = 0;
        reverse(a.begin(), a.end());
        string s = "";
        for(int i = 0; i < a.size(); i ++ ){
            int num = p * (a[i] - '0') + cnt;
            if(num < 10){
                cnt = 0;
                s += (num + '0');
            }    
            else{
                cnt = num / 10;
                s += (num % 10 + '0');
            }  
        }
        if(cnt) s += (cnt + '0');
        //  去除可能的前缀0
        int i = s.size() - 1;
        while(i >= 0){
            if(s[i] != '0') break;
            i -- ;
        }
        if(i == -1)   return "0";
        string res = "";
        while(i >= 0){
            res += s[i -- ];
        }
        return res;
    }
    string add(string a, string b){
        reverse(a.begin(), a.end());
        reverse(b.begin(), b.end());
        int cnt = 0, i;
        string s = "";
        for(i = 0; i < a.size() && i < b.size(); i ++ ){
            int num = a[i] + b[i] - 2 * '0' + cnt;
            if(num < 10){
                cnt = 0;
                s += (num + '0');
            }    
            else{
                cnt = 1;
                s += (num - 10 + '0');
            }
        }
        while(i < a.size()){
            int num = a[i] - '0' + cnt;
            if(num < 10){
                cnt = 0;
                s += (num + '0');
            }    
            else{
                cnt = 1;
                s += (num - 10 + '0');
            }
            i ++ ;
        }
        while(i < b.size()){
            int num = b[i] - '0' + cnt;
            if(num < 10){
                cnt = 0;
                s += (num + '0');
            }
            else{
                cnt = 1;
                s += (num - 10 + '0');
            }
            i ++ ;
        }
        if(cnt)     s += (cnt + '0');
        reverse(s.begin(), s.end());
        return s;
    }
    string multiply(string num1, string num2) {
        if(num1 == "0" || num2 == "0")  return "0";
        string res = "0";
        reverse(num2.begin(), num2.end());
        for(int i = 0; i < num2.size(); i ++ ){
            int p = num2[i] - '0';
            string tmp = mul(num1, p);
            for(int mov = 1; mov <= i; mov ++ )  tmp += '0';
            res = add(res, tmp);
        }
        return res;
    }
};