<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)
    {
        int index1=num1.size()-1, index2=num2.size()-1;
        string ans;
        int carry=0, sum;
        
        while(index2>=0)
        {
            sum=(num1[index1]-'0')+(num2[index2]-'0')+carry;
            carry=sum/10;
            char c='0'+sum%10;
            ans=c+ans;
            index2--, index1--;
        }

        while(index1>=0)
        {
            sum=(num1[index1]-'0')+carry;
            carry=sum/10;
            char c='0'+sum%10;
            ans=c+ans;
            index1--;
        }

        if(carry)
            ans='1'+ans;
            
        return ans;
    }

    string addStrings(string num1, string num2) {
        ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
        if(num1.size()<num2.size())
            return add(num2, num1);
        else
            return add(num1, num2);
    }
};
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