Тестовое задание, помогите пожалуйста 20 минут осталось)

package com.study;

import java.util.Stack;





public class Solution {



  public static void main(String[] args) {

     String first = "15555005";
     String second = "99";
     System.out.println(sum(first, second));
  }


  public static String sum(String first, String second){

    Stack<Integer> firstNumberDigits = new Stack<>();
    Stack<Integer> secondNumberDigits = new Stack<>();
    StringBuilder result = new StringBuilder();

    for(int i = 0 ; i<first.length(); i++){
    firstNumberDigits.push(Character.getNumericValue(first.charAt(i)));
    }
    for(int i = 0; i<second.length(); i++){
      secondNumberDigits.push(Character.getNumericValue(second.charAt(i)));
    }


    System.out.println(firstNumberDigits);
    System.out.println(secondNumberDigits);


    int overflow = 0;

    while(! firstNumberDigits.empty() && ! secondNumberDigits.empty()){
      int sum = firstNumberDigits.pop() + secondNumberDigits.pop() + overflow;
      if(sum >9){
        result.append(sum%10);
        overflow = 1;
      } else {
        result.append(sum);
        overflow = 0;
      }
    }

    while (! firstNumberDigits.empty()){
      int digit = firstNumberDigits.pop() + overflow;
      if(digit>9){
        result.append(digit%10);
        overflow = 1;
      } else {
        result.append(digit);
        overflow = 0;
      }

    }

    while(! secondNumberDigits.empty()){
      int digit = secondNumberDigits.pop() + overflow;
      if(digit>9){
        result.append(digit%10);
        overflow = 1;
      } else {
        result.append(digit);
        overflow = 0;
      }
    }

    if(overflow == 1)
        result.append(1);
    return result.reverse().toString();
  }

}

String a = "123";
 String b = "23";
 int [] digitsA = convertToIntArray(a.toCharArray()); // метод с fori ... arr[i] = Character.digit(temp[i], 10);
 int [] digitsB = convertToIntArray(b.toCharArray());

 int [] max = digitsA.length > digitsB.length ? digitsA : digitsB;
 int [] min = digitsA.length > digitsB.length ? digitsB : digitsA;

 int [] temp =  new int[max.length];

 System.arraycopy(min, 0, temp,max.length - min.length, min.length);
 StringBuilder result = new StringBuilder();

 int stage = 0;
 for (int i = max.length - 1; i >= 0; i--) {
     int r  = max[i] + temp[i] + stage;
     if (r >= 10) {
         stage = 1;
         r %= 10;
     }
     else stage = 0;
     result.insert(0, r);
 }
 System.out.println((stage == 0 ? "" : 1) + result.toString());