A10806. 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 $m$ ( $0<=n<m<=200000$ ) — 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.

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 $[3,7,4,6,8,0]$ .