C. Vulnerable Kerbals

Codeforces

IDCF800C

Time2000ms

Memory256MB

Difficulty—

constructive algorithmsmathnumber theory

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 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 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. [samples] ## 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 \[3, 7, 4, 6, 8, 0\].

Samples

Input #1

0 5

Output #1

5
1 2 4 3 0

Input #2

3 10
2 9 1

Output #2

6
3 9 2 9 8 0

API Response (JSON)

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