<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 n= a.length();
        int m= b.length();

        int carry=0;
        string res=""; 

        while(n>0 || m>0 || carry){

            int sum=0;

            if(n>0){
                sum+= a[n-1]-'0';
                n--;
            }
            if(m>0){
                sum+= b[m-1]-'0';
                m--;
            }

            sum+= carry;
            carry= sum/2;

            res+= to_string(sum%2);
        }      

        reverse(res.begin(), res.end());
        return res;
    }
};
10000