return bigger string value

#include <iostream>
using namespace std;

string bigger(string, string);

int main()
{
    cout << bigger("9995", "9996") << endl;
    return 0;
}

string bigger(string a, string b)
{
    if(a == b) return a;
    if(a.length() != b.length())
        return ((a.length() > b.length()) ? (a) : (b));
    int i = 0;
    while(a[i] == b[i])
        i++;
    return ((a[i] > b[i]) ? (a) : (b));
}