It is difficult to participate in Olympiads when you do not understand how they can help you in the future. Thus, after another failure, the spirit in the team dropped and the wish to compose Olympiads disappeared completely. The coach noticed that in time and decided to do something about it – after all, he understood what participation in such events could lead to. After much thought, he realized – you just need to show the team its prospects! Then, for simplicity, he presented all possible career development options arising after participating in the Olympiads in the form of a root tree. Each of its node was some position in a prestigious IT company, and the edges were drawn between positions only if career growth was possible from one position to another. Naturally, participation in the Olympiads made it easier to move up that tree, and the coach hurried up to show the tree to the team!
However, not all was as simple as that. The fact was that the team had absolutely no knowledge of those difficult positions and transitions. Therefore, the coach needed to choose several positions with beautiful and loud names and tell the team that after participating in the Olympiads, they could take up those positions. However, that choice was also limited. The fact was that the team was quite friendly and didn't want to occupy too diverse positions within the company. Therefore, they were to be selected in such a way that the highest position, from which one could still get into each of the selected ones, was far from the root as possible.
Help the coach to motivate the guys — find the necessary set of positions.
Formally speaking, you are given a rooted tree with N vertices, and you need to choose K vertices so that their least common ancestor could be as far from the root as possible.
The smallest common ancestor of several vertices is such a vertex that its distance from the root is maximal and from it one could get to any of the selected vertices if moving in the direction from the root.
In the first line of the input you are given two numbers — N and K (1 ≤ K ≤ N ≤ 105) — the number of positions in general and the number of positions that the coach should find.
The next line gives you N - 1 number, each of which does not exceed N. The i-th of them contains the number of the position from which one can go up to the i + 1-th position. Position 1 is considered to be the root one. It is guaranteed that this structure is a tree rooted at the first vertex.
For an answer, type a single line of K numbers randomly — the numbers of the positions that the coach should choose, or - 1 if there is no answer. If there are several answers, it is allowed to output any of them.
5 2
5 1 1 1
5 2
9 3
6 9 1 9 4 9 4 1
4 6 2
In the second test, the graph looks like that:
The following triplets can also be output as an answer:
(5, 3, 7); (8, 4, 2); (9, 5, 7);
