<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:
    void solve(int i,int carry,string &num1,string &num2,string &ans){
        if(i<0){
            if(carry==0){
                return;
            }
            ans.push_back(carry+'0');
            return;
        }
        int x=num1[i]-'0';
        int y=num2[i]-'0';
        int sum=((x+y)+carry)%10;
        int c=((x+y)+carry)/10;
        solve(i-1,c,num1,num2,ans);
        ans.push_back(sum+'0');
    }
    string addStrings(string num1, string num2) {
       int x=num1.size();
       int y=num2.size();
       if(x<y){
        while(x<y){
           num1='0'+num1;
           x++;
        } 
        x=y;
       }
       if(y<x){
        while(y<x){
           num2='0'+num2;
           y++;
        } 
        y=x;
       }
       string ans="";
       solve(x-1,0,num1,num2,ans);
       return ans;
    }
};
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