<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 {
public:

 string addRE(string& num1,int p1,string& num2,int p2,int carry=0){
    //base case
    if(p1 < 0 && p2 < 0){
        if(carry != 0){
            return string(1,carry + '0');
        }
        return "";
    }
    //1st case
    int n1=(p1>=0?num1[p1]:'0')-'0';
    int n2=(p2>=0?num2[p2]:'0')-'0';
    int sum = n1+n2+carry;
    int digit = sum%10;
    carry = sum/10;
    string ans="";
    ans.push_back(digit+'0');

    //RE krega ab
    ans+=addRE(num1,p1-1,num2,p2-1,carry);
    return ans;
 }

    string addStrings(string num1, string num2) {
       string ans=addRE(num1,num1.size()-1,num2,num2.size()-1,0);
       reverse(ans.begin(),ans.end());
        return ans;
    }
};
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