A12694 | Tokitsukaze and Powers

Tokitsukaze is playing a room escape game designed by SkywalkerT. In this game, she needs to find out hidden clues in the room to reveal a way to escape.

After a while, she realizes that the only way to run away is to open the digital door lock since she accidentally went into a secret compartment and found some clues, which can be interpreted as:

- Only when you enter $n$ possible different passwords can you open the door;
- Passwords must be integers ranged from $0$ to $(m - 1)$ ;
- A password cannot be $x$ ( $0 \leq x < m$ ) if $x$ and $m$ are not coprime (i.e. $x$ and $m$ have some common divisor greater than $1$ );
- A password cannot be $x$ ( $0 \leq x < m$ ) if there exist non-negative integers $e$ and $k$ such that $p^e = k m + x$ , where $p$ is a secret integer;
- Any integer that doesn't break the above rules can be a password;
- Several integers are hidden in the room, but only one of them can be $p$ .

Fortunately, she finds that $n$ and $m$ are recorded in the lock. However, what makes Tokitsukaze frustrated is that she doesn't do well in math. Now that she has found an integer that is suspected to be $p$ , she wants you to help her find out $n$ possible passwords, or determine the integer cannot be $p$ .

The only line contains three integers $n$ , $m$ and $p$ ( $1 \leq n \leq 5 \times 10^5$ , $1 \leq p < m \leq 10^{18}$ ).

It is guaranteed that $m$ is a positive integer power of a single prime number.

If the number of possible different passwords is less than $n$ , print a single integer $-1$ .

Otherwise, print $n$ distinct integers ranged from $0$ to $(m - 1)$ as passwords. You can print these integers in any order. Besides, if there are multiple solutions, print any.