<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) {
        std::deque<char> ws;
        auto carry = 0;
        int i1 = a.size() - 1;
        int i2 = b.size() - 1;
        while (i1 >= 0 || i2 >= 0 || carry) {
            const auto sum = (i1 >= 0 ? a[i1] - '0' : 0) + (i2 >= 0 ? b[i2] - '0': 0) + carry;
            ws.push_front('0' + (sum % 2));
            carry = sum >> 1;
            --i1;
            --i2;
        }
        return std::string(ws.begin(), ws.end());        
    }
};
9000