class Solution {
public:
    string addBinary(string a, string b) {
        string res;
        int carry = 0;
        int n = a.size(),m = b.size();
        for(int i = a.size()-1,j=b.size()-1;i>=0 || j>=0;i--,j--){
            int t1 = i < 0 ? 0 : (a[i] - '0'); 
            int t2 = j < 0 ? 0 : (b[j] - '0');
            int s = t1+t2+carry;
            int u  = s % 2;
            res = to_string(u) + res;
            carry = s /= 2;
        }
        if(carry){
            res = "1"+res;
        }

        return res;
    }
};