<p>Given two non-negative integers <code>num1</code> and <code>num2</code> represented as strings, return the product of <code>num1</code> and <code>num2</code>, also represented as a string.</p>

<p><strong>Note:</strong>&nbsp;You must not use any built-in BigInteger library or convert the inputs to integer directly.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> num1 = "2", num2 = "3"
<strong>Output:</strong> "6"
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> num1 = "123", num2 = "456"
<strong>Output:</strong> "56088"
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num1.length, num2.length &lt;= 200</code></li>
	<li><code>num1</code> and <code>num2</code> consist of digits only.</li>
	<li>Both <code>num1</code> and <code>num2</code>&nbsp;do not contain any leading zero, except the number <code>0</code> itself.</li>
</ul>

class Solution:
    def multiply(self, num1: str, num2: str) -> str:
        if num1 == "0" or num2 == "0":
            return "0"
        
        len1, len2 = len(num1), len(num2)
        result = [0] * (len1 + len2)
        
        for i in range(len1 - 1, -1, -1):
            for j in range(len2 - 1, -1, -1):
                mul = (ord(num1[i]) - ord('0')) * (ord(num2[j]) - ord('0'))
                p1, p2 = i + j, i + j + 1
                sum_ = mul + result[p2]
                result[p2] = sum_ % 10
                result[p1] += sum_ // 10
        
        result_str = ''.join(map(str, result))
        return result_str.lstrip('0')

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