In mathematics, the dihedral group is the group of symmetries of a regular -gon. Rotations and reflections are elements of , and in fact all elements of the dihedral group can be expressed as a series of rotations and reflections. Elements of act on the -gon by permuting its vertices. For example, consider a regular pentagon with vertices initially labeled (clockwise, starting from the top):
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Applying the above three dihedral actions to the pentagon (a rotation, reflection, and then another rotation) produces the following relabelings of the pentagon’s vertices:
You are given an arbitrary clockwise labeling of the vertices of a regular -gon using the integers through , and a second sequence to test. Determine whether it’s possible to apply some series of dihedral actions to the -gon so that the test sequence appears as a contiguous clockwise sequence of vertex labels on the transformed polygon.
输入格式
The first line of input has two integers and , () where is the number of vertices of the polygon and is the length of the sequence to be tested.
The next line contains space-separated integers (). This is the initial labeling of the polygon vertices. It is guaranteed that each integer from to appears exactly once.
The next line contains space-separated integers (). This is the sequence to be tested.
输出格式
Output a single integer, which is if the test sequence could appear as a contiguous sequence of vertex labels after applying some series of dihedral actions to the initial polygon, and otherwise.
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