class Solution {

 public:

     string multiply_one_digital(char c, string num2, int tail){

         string result;

         for(int i = ; i < tail; i ++) {

             result.push_back('');

         }

         int carry = ;

         for(int i = num2.size() - ; i >= ; i-- ) {

             int one_result = (c - ) * (num2[i] - ) + carry;

             carry = one_result/;

             char current_digital = one_result %  + ;

             result.insert(result.begin(),current_digital);

         }

         if(carry > )

             result.insert(result.begin(), (char)(carry + ));

         return result;

     }

     string multiply(string num1, string num2) {

         // Note: The Solution object is instantiated only once and is reused by each test case.

         string result;

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

             return result;

         if((num1.size() ==  && num1[] == '') ||

             (num2.size() ==  && num2[] == '')) {

             result.push_back('');

             return result;

         }

         vector<string> tmp_results;

         for(int i = num1.size() - ; i >= ; i -- ) {

             if(num1[i] == '')

                 continue;

             tmp_results.push_back(multiply_one_digital(num1[i], num2, num1.size() -  - i));

         }

         //add all temporary results

         string last_tmp_result = tmp_results[tmp_results.size() - ];

         int carry = ;

         for(int i = ; i < last_tmp_result.size(); i ++ ){

             int one_result = ;

             for( auto item: tmp_results) {

                 if(i > item.size() - )

                     continue;

                 one_result += (item[item.size() - - i] - );

             }

             one_result += carry;

             carry = one_result/;

             char current_digital = one_result %  + ;

             result.insert(result.begin(),current_digital);

         }

         if(carry > )

             result.insert(result.begin(), (char)(carry + ));

         return result;

     }

 };