Multiplying long integers

#include <string>
#include <iostream>
#include <algorithm>
using namespace std;

intmain()
{
	string s1 = "";
	string s2 = "";
	string product = "";

	//windows Ctrl+Z and Enter to end input
	//linux Ctrl+D end input
	while (cin >> s1 >> s2)
	{
		//cin >> s1 >> s2;
		//s1 = "98765432123";
		//s2 = "12345678987";

		int len1 = s1.size();
		int len2 = s2.size();
		int carry = 0;
		int remain = 0;
		product.resize(len1 + len2);//Maximum length of the product
		reverse(s1.begin(), s1.end());
		reverse(s2.begin(), s2.end());

		for (int i = 0; i < len1; i++)
		{
			for (int j = 0; j < len2; j++)
			{
				int tmp = (s1[i] - '0') * (s2[j] - '0') + product[i+j];

				carry = tmp / 10;
				remain = tmp % 10;
				product[i + j + 1] += carry;
				product[i + j] = remain;
			}
		}

		if (product[len1+len2-1]==0)//There is no carry at the end, the highest bit is 0
			product.resize(product.size() - 1);


		reverse(product.begin(), product.end());
		for (int i = 0; i < product.size(); i++)
		{
			cout << char(product[i] + '0');
		}
		cout << endl;

		//---------------------------------------------
		s1 = "";
		s2 = "";
		product = "";
	}

    return 0;
}