class Solution {
public:
    string addBinary(string a, string b) {
        int len_a = a.size() - 1, len_b = b.size() - 1;
        int dif = abs(len_a - len_b);
        string prev = "";
        for (int i = 0; i < dif; ++i) prev += ‘0‘;
        if (len_a < len_b) a = prev + a;
        else b = prev + b;
        int len = a.size(), step = 0;
        vector<int> v;
        for (int i = len - 1; i > -1; --i) {
            step += a[i] + b[i] - (‘0‘ << 1);
            v.push_back(step % 2);
            step = step >> 1;
        }
        if (step) v.push_back(step % 2);
        string res;
        for (int i = v.size() - 1; i > -1; --i) {
            res += (‘0‘ + v[i]);
        }
        return res;
    }
};