<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 &e1, int &e2, string &ans, int &carry,string num1, string num2)
    {
        if(e1<0 || e2<0)
        {
            return;
        }
        int a1=num1[e1]-'0';
        int a2=num2[e2]-'0';
        ans.push_back(((a1+a2+carry)%10)+'0');
        carry=(a1+a2+carry)/10;
        e1--;
        e2--;
        solve(e1,e2,ans,carry,num1,num2);
    }
    string addStrings(string num1, string num2) {
        int len1=num1.length();
        int len2=num2.length();
        string ans="";
        int carry=0;
        int e1=len1-1;
        int e2=len2-1;
        solve(e1,e2,ans,carry,num1,num2);
        while(e1>=0)

        { 
            int a1=num1[e1]-'0';
            ans.push_back(((a1+carry)%10)+'0');
        carry=(a1+carry)/10;
        e1--;
        // if(carry!=0)
        // {
        //     ans.push_back(carry+'0');
        //     carry=0;
        // }

        }
         while(e2>=0)
        {
            int a1=num2[e2]-'0';
             ans.push_back(((a1+carry)%10)+'0');
        carry=(a1+carry)/10;
        e2--;
        // if(carry!=0)
        // {
        //     ans.push_back(carry+'0');
        //     carry=0;
        // }

        }
         if(carry)
        {
            ans.push_back(carry+'0');
        }
        string reversed(ans.rbegin(), ans.rend());
        return reversed;
    }
};
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