<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,string& num2,int i,int j,int ans = 0,int carry = 0,string str = "") {
        if(i < 0 && j < 0) {
            if(carry != 0) {
                str.push_back(carry + '0');
                carry = 0;
            }
                reverse(str.begin(),str.end());
                return str;
        }
        else if(j < 0) {
            ans = (num1[i] - '0') + carry;
            carry = 0;
        }
        else if(i < 0) {
            ans = (num2[j] - '0') + carry;
            carry = 0;
        }         
        else {
            ans = (num1[i] - '0') + (num2[j] - '0') + carry;
            carry = 0;
        }  
         if(ans > 9) {
             carry = ans / 10;
            ans = ans % 10;   
        }
        str.push_back(ans + '0');  
        return addRE(num1,num2,--i,--j,ans,carry,str);
    }
    string addStrings(string num1, string num2) {
        return addRE(num1,num2,num1.length()-1,num2.length()-1);
    }
};
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