CF772C Vulnerable Kerbals

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.

The first line of input contains two integers $ n $ and $ m $ ( $ 0

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.

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] $ .