<p>Given two binary strings <code>a</code> and <code>b</code>, return <em>their sum as a binary string</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> a = "11", b = "1"
<strong>Output:</strong> "100"
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> a = "1010", b = "1011"
<strong>Output:</strong> "10101"
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= a.length, b.length &lt;= 10<sup>4</sup></code></li>
	<li><code>a</code> and <code>b</code> consist&nbsp;only of <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code> characters.</li>
	<li>Each string does not contain leading zeros except for the zero itself.</li>
</ul>

class Solution {
public:
    string addBinary(string a, string b) {
        int ai = a.length()-1;
        int bi = b.length()-1;
        string res;

        int c = 0;
        while (ai >= 0 || bi >= 0) {
            int anum = ai >= 0 ? (a[ai]-'0') : 0;
            int bnum = bi >= 0 ? (b[bi]-'0') : 0;

            int s = (anum + bnum + c) & 1;
            c = ((anum + bnum + c) & 2) >> 1;
            
            res = (s ? "1" : "0") + res;

            ai--;
            bi--;
        }

        if (c == 1) {
            res = "1" + res;
        }

        return res;
    }
};
11000