In the first line, output a single number $n$ ($1 \leq n \leq 1\,000$) --- the minimum number of operations of pressing one of the buttons needed to reach the balance $x$.

In the second line, output $n$ integers $a_1, a_2, \dots, a_n$ ($1 \leq a_i \leq 2$) --- the buttons in the order they need to be pressed.

If it is impossible to obtain a balance exactly equal to $x$ using the given buttons, output $-1$.