Sasha lives in a big happy family. At the Man's Day all the men of the family gather to celebrate it following their own traditions. There are n men in Sasha's family, so let's number them with integers from 1 to n.
Each man has at most one father but may have arbitrary number of sons.
Man number A is considered to be the ancestor of the man number B if at least one of the following conditions is satisfied:
Of course, if the man number A is an ancestor of the man number B and A ≠ B, then the man number B is not an ancestor of the man number A.
The tradition of the Sasha's family is to give gifts at the Man's Day. Because giving gifts in a normal way is boring, each year the following happens.
This year you have decided to help in organizing celebration and asked each of the n men, who do they want to give presents to (this person is chosen only among ancestors). Are you able to make a list of candidates, such that all the wishes will be satisfied if they give gifts according to the process described above?
In the first line of the input two integers n and m (0 ≤ m < n ≤ 100 000) are given — the number of the men in the Sasha's family and the number of family relations in it respectively.
The next m lines describe family relations: the (i + 1)^{th} line consists of pair of integers p_{i} and q_{i} (1 ≤ p_{i}, q_{i} ≤ n, p_{i} ≠ q_{i}) meaning that the man numbered p_{i} is the father of the man numbered q_{i}. It is guaranteed that every pair of numbers appears at most once, that among every pair of two different men at least one of them is not an ancestor of another and that every man has at most one father.
The next line contains n integers a_{1}, a_{2}, ..., a_{n} (1 ≤ a_{i} ≤ n), i^{th} of which means that the man numbered i wants to give a gift to the man numbered a_{i}. It is guaranteed that for every 1 ≤ i ≤ n the man numbered a_{i} is an ancestor of the man numbered i.
Print an integer k (1 ≤ k ≤ n) — the number of the men in the list of candidates, in the first line.
Print then k pairwise different positive integers not exceeding n — the numbers of the men in the list in an order satisfying every of the men's wishes, one per line.
If there are more than one appropriate lists, print any of them. If there is no appropriate list print - 1 in the only line.
3 2
1 2
2 3
1 2 1
-1
4 2
1 2
3 4
1 2 3 3
3
2
1
3
The first sample explanation:
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