<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 add(string& num1, string& num2, string& s, int i, int j, int c){
        if(i < 0 && j < 0 && c == 0){
            return "";
        }
        int n1, n2;
        if(i >= 0)
            n1 = num1[i] - '0';
        else
            n1 = 0;
        if(j >= 0)
            n2 = num2[j] - '0';
        else
            n2 = 0;
        int sum = n1 + n2 + c;
        c = sum/10;

        s = add(num1, num2, s, i-1, j-1, c) + to_string(sum%10);
        return s;
    }
    string addStrings(string num1, string num2) {
        int i = num1.length()-1;
        int j = num2.length()-1;
        string s1 = "";
        string s = add(num1, num2, s1, i, j, 0);
        return s;
    }
};
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