mutiply strings

class Solution {
public:
    string multiply(string num1, string num2) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        vector<int> r( num1.length()+num2.length(),0);
        int c = 0;
        for(int i=num1.length()-1;i>=0;i--)
        {
            for(int j=num2.length()-1;j>=0;j--)
            {
                int k = num1.length()-1-i+num2.length()-1-j;
                r[k] += (num1[i]-'0')*(num2[j]-'0');
                c = r[k]/10;
                r[k] = r[k]%10;
                if( c > 0 )
                    r[k+1] += c;
            }
        }
        
        int i=r.size()-1;
        while( r[i] == 0 && i>0) i--;
        string s="";
        while( i>=0 )
            s += r[i--] + '0';
        
        return s;
        
        
    }
};