<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 {
public:
    string multiply(string num1, string num2) {
        if(num1=="0"||num2=="0") return "0";
        vector<vector<int>> prods;
        reverse(num1.begin(),num1.end());
        reverse(num2.begin(),num2.end());
        for(int i=0;i<num2.size();i++){
            int carry=0;
            vector<int> pass(i,0);
            for(auto n1:num1){
                int val = ((num2[i]-'0')*(n1-'0'))+carry;
                carry = val/10;
                pass.emplace_back(val%10);
            }
            if(carry!=0){
                pass.emplace_back(carry);
            }
            prods.push_back(pass);
        }
        string output="";
        int carry = 0;
        for(int j=0;j<prods.back().size();j++){
            int val = 0;
            for(int k=0;k<prods.size();k++){
                if(prods[k].size()>j){
                    val += prods[k][j];
                }
            }
            val +=carry;
            
            output += '0'+(val%10);
            carry=val/10;
        }
        if(carry!=0){
            output+='0'+carry;
        }
        reverse(output.begin(),output.end());
        return output;
        
    }
};
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