Description: You 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. Input Format: The 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. Output Format: On 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. Note: For 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].