Gunwoo is currently at house $A$ and wants to move to house $B$. He can use a teleportation device to move between houses. This device has $N$ buttons, and an integer $a_i$ is written on the $i$-th button. Pressing $i$-th button moves him from house $x$ to house $x \vee a_i$. Here, $\vee$ denotes the bitwise OR operation. Gunwoo can use this device at most $100$ times. Determine whether he can move from house $A$ to house $B$, and if so, find the sequence of buttons he needs to press.

The first line contains integers $N, A, B$ separated by a space. The second line contains $N$ integers $a_1, a_2, \ldots, a_N$ separated by a space.

If Gunwoo can go from house $A$ to house $B$, print $k$, the number of times the device will be used on the first line. Then, print the indices of the buttons to press in order on the second line, separated by a space. If he cannot go to house $B$, print -1. Here, $k$ must be an integer between $0$ and $100$, inclusive. If there are multiple valid answers, you may print any of them.

• $1 \le N \le 10^5$
• $0 \le A, B \le 10^9$
• $1 \le a_i \le 10^9$ $(1\leq i \leq N)$