Add Binary

Given two binary strings, return their sum (also a binary string).
For example,
a = "11"
b = "1"
Return "100".

Solution: '1'-'0' = 1.

class Solution {
public:
    string addBinary(string a, string b) {
        int N = a.size();
        int M = b.size();
        int K = max(M, N);
        string res(K,' ');
        int carry = 0;
        int i = N - 1, j = M - 1, k = K - 1;
        while(i >= 0 || j >= 0) {
            int sum = carry;
            if(i >= 0) sum += a[i--] - '0';
            if(j >= 0) sum += b[j--] - '0';
            carry = sum / 2;
            res[k--] = sum % 2 + '0'; 
        }
        if(carry == 1) res.insert(res.begin(), '1');
        return res;
    }
};