<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:
    def addBinary(self, a: str, b: str) -> str:
        if len(a) - len(b) > 0:
            b = "0" * (len(a) - len(b)) + b
        elif len(b) - len(a) > 0:
            a = "0" * (len(b) - len(a)) + a

        s = ""
        i = len(a) - 1
        divide = 0
        while i >= 0:
            res = int(a[i]) + int(b[i]) + divide
            divide = res // 2
            remainder = res % 2
            s = str(remainder) + s
            i -= 1

        if divide == 1:
            s = "1" + s
        
        return s
        
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