<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) {
        vector<int> aa;
        vector<int> bb;
        for(int i=0; i< a.length(); i++)
        {
            int num = a[i] - '0';
            aa.push_back(num);
            
        }
        for(int i=0; i< b.length(); i++)
        {
            int num = b[i] - '0';
            bb.push_back(num);

        }

        int n = aa.size()-1;
        int m = bb.size()-1;
        int c = 0;
        vector<int> ans;
        while(n >= 0  &&  m >= 0)
        {
            int sum = aa[n] + bb[m] + c;
            int let  = sum%2;
            ans.push_back(let);
            c = sum/2;
            n--;
            m--;
        }
        while(n >= 0 )
        {
            int sum = aa[n] + c;
            int let  = sum%2;
            ans.push_back(let);
            c = sum/2;
            n--;
            
        }
        while(m >= 0 )
        {
            int sum = bb[m] + c;
            int let  = sum%2;
            ans.push_back(let);
            c = sum/2;
            m--;
            
        }
        if(c>0)
        {
            ans.push_back(c);
        }
        reverse(ans.begin(),ans.end());
        string the = "";
        for(int i=0; i< ans.size(); i++)
        {
            char p = ans[i]+'0';
            the += p;

        }
        return the;

    }
};
9200