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class Solution {
    public String addBinary(String a, String b) {
        StringBuilder sb = new StringBuilder();

        int i = a.length() - 1;
        int j = b.length() - 1;
        int carry = 0;
        while (i >= 0 || j >= 0) {
            int sum = carry;
            if (i >= 0) {
                sum += a.charAt(i) - '0';
                i--;
            }
            if (j >= 0) {
                sum += b.charAt(j) - '0';
                j--;
            }
            if (sum >= 2) {
                carry = 1;
            } else {
                carry = 0;
            }
            sb.append(sum % 2);

        }

        if (carry != 0) {
            sb.append(carry);
        }
        return sb.reverse().toString();
    }
}
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