Question 82
On the blackboard $n$ nonnegative integers have been written, such that their greatest common divisor is equal to $1$. In one step we can erase two numbers $x$, $y$ such that $x \ge y$, and replace them with numbers $x - y$, $2y$. Determine, for which sequences of original $n$ integers one can lead to a situation, in which $n - 1$ numbers on the blackboard are zeroes.