[LeetCode] Add Binary

Given two binary strings, return their sum (also a binary string).

For example,
a = "11"
b = "1"
Return "100".

public class Solution {
    public String addBinary(String a, String b) {
		int carry = 0;
		int sum = 0;
		StringBuilder result = new StringBuilder();
		int i;

		for (i = 0; i < a.length() && i < b.length(); i++) {
			int m = a.charAt(a.length() - i - 1) - '0';
			int n = b.charAt(b.length() - i - 1) - '0';

			sum = (carry + m + n) % 2;
			carry = (carry + m + n) / 2;

			result.insert(0, sum + "");
		}

		for (; i < a.length(); i++) {
			int m = a.charAt(a.length() - i - 1) - '0';

			sum = (carry + m) % 2;
			carry = (carry + m) / 2;

			result.insert(0, sum + "");
		}

		for (; i < b.length(); i++) {
			int m = b.charAt(b.length() - i - 1) - '0';

			sum = (carry + m) % 2;
			carry = (carry + m) / 2;

			result.insert(0, sum + "");
		}

		if (carry == 1) {
			result.insert(0, carry + "");
		}

		return result.toString();
	}
}