C++ simple code problem:

I am trying to write a small program that finds the product of two numbers with a do-while.

int nmbr1, nmbr2;

int product = 1;

do {

cout << "Enter a number: " << endl;

cin >> nmbr1 >> nmbr2;

product = nmbr1 ^ nmbr2;

} while (nmbr1 != 0);

cout << "Total sum is: " << product

<< endl;

system("Pause");

return 0;

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Is the problem with the while statement? It keeps returning 0 and the input nature in the command prompt is strange as well.