Vulnerable Kerbals

题意翻译

给出m,n，再给一个m个数的集合让你构造一个序列满足以下的条件： 1.这个序列的所有数都在0-m-1之间（含） 2.这个数列的所有前缀积都不同 3.所有的前缀积都不能出现在给你的集合中 4.最大化这个序列的长度 输出任意满足条件的序列。

题目描述

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.

输入输出格式

输入格式

The first line of input contains two integers $ n $ and $ m $ ( $ 0<=n&lt;m<=200000 $ ) — 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.

输出格式

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.

输入输出样例

输入样例 #1

0 5

输出样例 #1

5
1 2 4 3 0

输入样例 #2

3 10
2 9 1

输出样例 #2

6
3 9 2 9 8 0

说明

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] $ .