<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(string a, string b, int carry, string & ans, int i, int j){
        if(i<0 && j<0 && carry==0){
            return;
        }
        int fi=0,se=0;
        if(i>=0){
            fi=a[i]-'0';
        }
        if(j>=0){
            se=b[j]-'0';
        }
        int sum=fi+se+carry;
        carry=sum/10;
        int las=sum%10;
        ans.push_back(las+'0');
        solve(a,b,carry,ans,i-1,j-1);
        
    }
    string addStrings(string num1, string num2) {
        string ans="";
        solve(num1,num2,0,ans,num1.size()-1,num2.size()-1);
        reverse(ans.begin(),ans.end());
        return ans;

        
    }
};
123106