C. Vulnerable Kerbalstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an integer m, and a list of n distinct integers between 0 and m - 1.You would like to construct a sequence satisfying the properties:  Each element is an integer between 0 and m - 1, inclusive.  All prefix products of the sequence modulo m are distinct.  No prefix product modulo m appears as an element of the input list.  The length of the sequence is maximized. Construct any sequence satisfying the properties above.InputThe first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus.If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist.OutputOn the first line, print the number k, denoting the length of your sequence.On the second line, print k space separated integers, denoting your sequence.ExamplesInput0 5Output51 2 4 3 0Input3 102 9 1Output63 9 2 9 8 0NoteFor the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0].For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0].
Input0 5
Output51 2 4 3 0
['constructive algorithms', 'dp', 'graphs', 'math', 'number theory', '*2300']