Going Home

After the collider exploded, Spider-Man Miles Morales ended up in a parallel universe. Realizing he needed help, he quickly found Peter Parker, the Spider-Man of this universe, and told him his story. After analyzing the collider blueprints Miles had accidentally taken with him and many other parameters, they found that Miles is in universe number $A$ and his own universe is number $B$. After several months, they built a device for traveling between universes that can take Miles home. The device has $n$ buttons with numbers $a_1, a_2, \ldots, a_n$. Pressing the button $a_i$ moves you from the current universe $x$ to universe $x \lor a_i$ ($\lor$ is bitwise OR). However, their resources were limited, so the device has enough charge for only $100$ moves. Miles and Peter are trying to work out the order in which to press the buttons to send Miles home. Help them!

The first line contains three integers $n$, $A$, and $B$: the number of buttons, the universe where Miles is now, and the universe where he needs to return ($1 \le n \le 10^5$, $0 \le A, B \le 10^9$). The second line contains $n$ integers $a_1, a_2, \ldots, a_n$, the numbers written on the buttons ($1 \le a_i \le 10^9$).

If Miles cannot get home, print $-1$ on a single line. Otherwise, print the number $k$ of button presses on the first line ($0 \le k \le 100$), and on the second line print the $k$ button numbers separated by spaces, in the order they should be pressed. If there are several answers, print any of them.

In the first example, press button 1 first to move from universe 2 to universe $2 \lor 3 = 3$. Then press button 4 to move from universe 3 to universe $3 \lor 10 = 11$.