<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) {
        vector<vector<int>> m;
        if(num1.size()<num2.size()){
            string s="";
            s=num1;
            num1=num2;
            num2=s;
        }
        //cout<<num1<<"   "<<num2<<endl;
        int c=0;
        for(int i=(num2.size()-1);i>=0;i--){
            int r=0;
            vector<int> v;
            for(int j=(num1.size()-1);j>=0;j--){
                //cout<<i<<"  "<<j<<endl;
                string k=string(1,num1[j]);
                string l=string(1,num2[i]);
                int a=stoi(k);
                int b=stoi(l);
                int x=a*b+r;
                r=x/10;
                x=x%10;
                v.push_back(x);
            }
            if(r!=0){
                v.push_back(r);
            }
            int h=num2.size()-c;
            if(r!=0){
                h--;
            }
            c++;
            while(h>0){
                v.push_back(0);
                h--;
            }
            reverse(v.begin(),v.end());
            int p=num2.size()-1-i;
            while(p>0){
                v.push_back(0);
                p--;
            }
            m.push_back(v);
        }
        for(int i=0;i<m.size();i++){
            for(int j=0;j<m[i].size();j++){
                cout<<m[i][j]<<" ";
            }
            cout<<endl;
        }
        cout<<endl;
        string s="";
        int r=0;
        for(int j=m[0].size()-1;j>=0;j--){
            int x=0;
            for(int i=0;i<m.size();i++){
                int a=m[i][j];
                x=x+a;
            }
            x=x+r;
            int b=x%10;
            r=x/10;
            //cout<<"x,b,r="<<x<<" "<<b<<" "<<r<<endl;
            s=to_string(b)+s;
            //cout<<s<<endl;
        }
        if(r!=0){
            s=to_string(r)+s;
        }
        int i=0;
        string result="";
        while(s[i]=='0'&&i<s.size()-1){
            i++;
        }
        while(i<s.size()){
            result=result+s[i];
            i++;
        }
        return result;
    }
};
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