給定兩個二進位制字串，返回他們的和（用二進位制表示）。

輸入為非空字串且只包含數字 1 和 0。

示例 1:

輸入: a = “11”, b = “1”
輸出: “100”
示例 2:

輸入: a = “1010”, b = “1011”
輸出: “10101”

class Solution {
public:
    string addBinary(string a, string b) {
        int len1 = a.size();
        int len2 = b.size();
        if(len1==0){
            return b;
        }
        if
 
(len2==0){
            return a;
        }
        string ret;
        int carry = 0;
        int index1 = len1-1;
        int index2 = len2-1;
        while(index1>=0&&index2>=0){
            int num = (a[index1]-'0')+(b[index2]-'0')+carry;
            carry = num/2;
            num = num%2;
            index1--;
            index2--;
            ret.insert(ret.begin(),num+'0'
 
);
        }
        if(index1<0&&index2<0){
            if(carry==1){
                ret.insert(ret.begin(),carry+'0');
                return ret;
            }
        }
        while(index1>=0){
            int num = (a[index1]-'0')+carry;
            carry = num/2;
            num = num%2
 
;
            index1--;
            ret.insert(ret.begin(),num+'0');
        }
        while(index2>=0){
            int num = (b[index2]-'0')+carry;
            carry = num/2;
            num = num%2;
            index2--;
            ret.insert(ret.begin(),num+'0');
        }
        if(carry==1){
            ret.insert(ret.begin(),carry+'0');

        }
         return ret;
    }
};