<p>Given two non-negative integers, <code>num1</code> and <code>num2</code> represented as string, return <em>the sum of</em> <code>num1</code> <em>and</em> <code>num2</code> <em>as a string</em>.</p>

<p>You must solve the problem without using any built-in library for handling large integers (such as <code>BigInteger</code>). You must also not convert the inputs to integers directly.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> num1 = &quot;11&quot;, num2 = &quot;123&quot;
<strong>Output:</strong> &quot;134&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num1 = &quot;456&quot;, num2 = &quot;77&quot;
<strong>Output:</strong> &quot;533&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num1 = &quot;0&quot;, num2 = &quot;0&quot;
<strong>Output:</strong> &quot;0&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num1.length, num2.length &lt;= 10<sup>4</sup></code></li>
	<li><code>num1</code> and <code>num2</code> consist of only digits.</li>
	<li><code>num1</code> and <code>num2</code> don&#39;t have any leading zeros except for the zero itself.</li>
</ul>

class Solution {
private:
    string addRE(string &num1, string &num2, int p1, int p2, int carry=0){

        if(p1 < 0 && p2 < 0 && carry == 0){ return ""; }

        int n1 = (p1 >= 0 ? num1[p1] : '0') - '0';
        int n2 = (p2 >= 0 ? num2[p2] : '0') - '0';
        
        int total = n1 + n2 + carry;
        int sum = total%10;
        carry = total/10;

        return addRE(num1, num2, p1-1, p2-1, carry).append(to_string(sum));
    }
public:
    string addStrings(string num1, string num2) {
        string res = addRE(num1, num2, num1.size()-1, num2.size()-1);
        return res;
    }
};
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