<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 addStrings(string num1, string num2) {
        int len1 = num1.size();
        int len2 = num2.size();
        
        string ret;
        int i1 = num1.size() - 1;
        int i2 = num2.size() - 1;
        int carryOn = 0;
        while (i1 >= 0 && i2 >= 0) {
            int res = num1[i1] - '0' + num2[i2] - '0' + carryOn;
            ret = res > 9 ? string(1, res - 10 + '0') + ret : string(1, res + '0') + ret;
            carryOn = res > 9 ? 1 : 0;
            --i1;
            --i2;
        }

        // after we get out, need to check carryOn, if it's 1, need to add to prefix's last char
        // if last char + 1 is greater than 10, keep going prefix. 
        // and we may need to add 1 at the beginning of prefix. 
        string prefix = len1 > len2 ? num1.substr(0, len1 - len2) : num2.substr(0, len2 - len1);
        int i = prefix.size() - 1;
        while (carryOn == 1 && i >= 0) {
            int r = prefix[i] - '0' + 1;
            if (r < 10) {
                carryOn = 0;
                prefix[i] = r + '0';
            } else {
                prefix[i] = r - 10 + '0';
                --i;
            }
        }

        if (carryOn == 1) {
            prefix = string(1, '1') + prefix;
        }
        ret = prefix + ret;
        return ret;
    }
};
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