高精度函数运行不了

string add (string a, string b){
    string c;
    int maxlen = max (a.length (), b.length ());
    reverse (a.begin (), a.end ());
    reverse (b.begin (), b.end ());
    for (int i = 0; i < maxlen; i++){
        int k = (a[i] - '0') + (b[i] - '0');
        c[i] = k % 10;
        c[i - 1] = k / 10;
    }
    return c;
}