D. Friendly Spiderstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputMars is home to an unusual species of spiders — Binary spiders.Right now, Martian scientists are observing a colony of n spiders, the i-th of which has a_i legs.Some of the spiders are friends with each other. Namely, the i-th and j-th spiders are friends if \gcd(a_i, a_j) \ne 1, i. e., there is some integer k \ge 2 such that a_i and a_j are simultaneously divided by k without a remainder. Here \gcd(x, y) denotes the greatest common divisor (GCD) of integers x and y.Scientists have discovered that spiders can send messages. If two spiders are friends, then they can transmit a message directly in one second. Otherwise, the spider must pass the message to his friend, who in turn must pass the message to his friend, and so on until the message reaches the recipient.Let's look at an example.Suppose a spider with eight legs wants to send a message to a spider with 15 legs. He can't do it directly, because \gcd(8, 15) = 1. But he can send a message through the spider with six legs because \gcd(8, 6) = 2 and \gcd(6, 15) = 3. Thus, the message will arrive in two seconds.Right now, scientists are observing how the s-th spider wants to send a message to the t-th spider. The researchers have a hypothesis that spiders always transmit messages optimally. For this reason, scientists would need a program that could calculate the minimum time to send a message and also deduce one of the optimal routes.  InputThe first line of input contains an integer n (2 \le n \le 3\cdot10^5) — the number of spiders in the colony.The second line of input contains n integers a_1, a_2, \ldots, a_n (1 \le a_i \le 3\cdot10^5) — the number of legs the spiders have.The third line of input contains two integers s and t (1 \le s, t \le n) —the spiders between which the message must be sent.OutputIf it is impossible to transmit a message between the given pair of spiders, print -1.Otherwise, in the first line of the output print the integer t (t \ge 1) — the number of spiders that participate in the message transmission (i. e. the minimum time of message delivery in seconds plus one). In the second line, print t different integers b_1, b_2, \ldots, b_t (1 \le b_i \le n) — the ids of the spiders through which the message should follow, in order from sender to receiver.If there are several optimal routes for the message, output any of them.ExamplesInput
7
2 14 9 6 8 15 11
5 6
Output
3
5 4 6 Input
7
2 14 9 6 8 15 11
5 7
Output
-1Input
7
2 14 9 6 8 15 11
5 5
Output
1
5
NoteThe first example is shown above. It shows that the message from the 5-th spider (with eight legs) to the 6-th spider (with 15 legs) is optimal to pass through the 4-th spider (with six legs).In the second example, the spider number 7 (with 11 legs) is not friends with anyone, so it is impossible to send him a message.
7
2 14 9 6 8 15 11
5 6

3 5 4 6 
['dfs and similar', 'graphs', 'math', 'number theory', 'shortest paths', '*1800']