{"problem":{"name":"C. Vulnerable Kerbals","description":{"content":"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 an","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF800C"},"statements":[{"statement_type":"Markdown","content":"You are given an integer _m_, and a list of _n_ distinct integers between 0 and _m_ - 1.\n\nYou would like to construct a sequence satisfying the properties:\n\n*   Each element is an integer between 0 and _m_ - 1, inclusive.\n*   All prefix products of the sequence modulo _m_ are distinct.\n*   No prefix product modulo _m_ appears as an element of the input list.\n*   The length of the sequence is maximized.\n\nConstruct any sequence satisfying the properties above.\n\n## Input\n\nThe first line of input contains two integers _n_ and _m_ (0 ≤ _n_ < _m_ ≤ 200 000) — the number of forbidden prefix products and the modulus.\n\nIf _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.\n\n## Output\n\nOn the first line, print the number _k_, denoting the length of your sequence.\n\nOn the second line, print _k_ space separated integers, denoting your sequence.\n\n[samples]\n\n## Note\n\nFor the first case, the prefix products of this sequence modulo _m_ are \\[1, 2, 3, 4, 0\\].\n\nFor the second case, the prefix products of this sequence modulo _m_ are \\[3, 7, 4, 6, 8, 0\\].","is_translate":false,"language":"English"}],"meta":{"iden":"CF800C","tags":["constructive algorithms","math","number theory"],"sample_group":[["0 5","5\n1 2 4 3 0"],["3 10\n2 9 1","6\n3 9 2 9 8 0"]],"created_at":"2026-03-03 11:00:39"}}