#87 teleport

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#87 teleport | DOJ

Authors: wookji

Time limit: 1000 ms
Python time limit: 3000 ms
Memory limit: 256 MB
Checker: CUSTOM
Solve threshold: 100

Statement

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.

Input

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.

Output

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.

Constraints

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

Subtasks

#	Score	Constraints
1	20	$N \le 20$
2	30	$0 \le A, B < 2^{15}$ , $1 \le a_i < 2^{15}$
3	50	No additional constraints.

Samples

Sample 1

Input

3 1 7
2 4 3

Output

2
1 2

Initially, he is at house $1$ . Pressing the 1st button moves him to house $3$ since $1 \vee 2 = 3$ . Pressing the 2nd button moves him to house $7$ since $3 \vee 4 = 7$ .

Sample 2

Input

2 1 4
4 2

Output

-1

The bit that is already turned on at the initial position $A=1$ is not turned on in $B=4$ . Since the bitwise OR operation cannot turn off this bit again, it is impossible to move to house $B$ .

Sample 3

Input

1 5 5
1

Output

He is at house $B$ from the beginning, so he does not need to press any buttons.

Editorial

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