Calculate the sum of 2 numbers in Mars

Martian Addition

#include <fstream>
#include <iostream>
#include <string>
using namespace std;
//Calculate the sum of 2 numbers in Mars.
int main()
{
    //ifstream cin("martian_addition.txt");
    string a,b;
    string s="0123456789abcdefghijk"; //more than 20 ! The key is 'k'.
    while(cin>>a>>b)
    {   
        bool m=false; //more digits
        while(a.size()!=b.size())
        {   
            a.size()<b.size()?(a="0"+a):(b="0"+b);  //equals the length.
        }   
        a="0"+a;b="0"+b;  //add '0' before
        for(int i=a.size()-1;i>0;i--)
        {   
            int n=s.find(a[i])+s.find(b[i]);
            if(n>=20&&i==1)
                m=true;
            a[i]=s[n%20];
            a[i-1]=s[(s.find(a[i-1])+n/20)];
        }   
        if(m) a[0]='1'; //add digit
        if(!m) a=a.replace(0,1,""); //remove '0'
        cout<<a<<endl;
    }   
    return 0;
}