Adding big number [THCS4 N1]

//Tran Viet Anh - 14:41PM
#include <iostream>
#include <string>

using namespace std;

int main()
{
    cout << "Input the first number: ";
    string num1; cin >> num1;
    cout << "Input the second number: ";
    string num2; cin >> num2;
    string result;
    if (num1.length() >= num2.length()) result = num1;
    else result = num2;
    int remember = 0;
    int i = num1.length() - 1, j = num2.length() - 1, k = result.length() - 1;
    while (i >= 0 || j >= 0)
    {
        int value;
        if (i >=0 && j >= 0)
            value = (num1[i] - 48) + (num2[j] - 48) + remember;
        else
            if (i >= 0)
                value = (num1[i] - 48) + remember;
            else
                value = (num2[j] - 48) + remember;
        remember = value / 10;
        result[k] = value % 10 + 48;
        i--; j--; k--;
    }
    cout << "Result: ";
    if (remember != 0) cout << 1;
    cout << result;
    return 0;
}