CF1190F.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 $x$ ($0 \leq x \lt m$) if $x$ and $m$ are not coprime (i.e. $x$ and $m$ have some common divisor greater than $1$);
• A password cannot be $x$ ($0 \leq x \lt m$) 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 $p$.

Tokitsukaze 正在玩一款由 SkywalkerT 设计的密室逃脱游戏。在该游戏中，她需要在房间中寻找隐藏线索，从而揭示逃脱的方法。

过了一段时间后，她意识到唯一的逃生方式是打开一扇数字门锁——因为她偶然进入了一个秘密隔间，并在那里发现了一些线索，这些线索可被解读为：

• 只有当输入 $n$ 个互不相同的密码时，才能打开这扇门；
• 密码必须是取值范围在 $0$ 到 $(m - 1)$（含端点）之间的整数；
• 若整数 $x$（其中 $0 \leq x < m$）与 $m$ 不互质（即 $x$ 与 $m$ 存在大于 $1$ 的公因数），则 $x$ 不能作为密码；
• 若存在非负整数 $e$ 和 $k$，使得 $p^e = k m + x$（其中 $p$ 是某个未知的整数），则整数 $x$（其中 $0 \leq x < m$）不能作为密码；
• 任何不违反上述规则的整数均可作为密码；
• 房间中隐藏着若干个整数，但其中仅有一个可能是 $p$。

幸运的是，她发现锁上已记录了 $n$ 和 $m$ 的值。然而令 Tokitsukaze 感到沮丧的是，她的数学不太好。如今她找到了一个疑似为 $p$ 的整数，希望你能帮她找出 $n$ 个可能的密码；若该整数不可能是 $p$，则请判定其不合法。

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

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

仅一行，包含三个整数 $n$、$m$ 和 $p$（$1 \leq n \leq 5 \times 10^5$，$1 \leq p \lt m \leq 10^{18}$）。

保证 $m$ 是某个单一素数的正整数幂。

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.

如果可能的不同密码数量少于 $n$，则输出单个整数 $-1$。

否则，输出 $n$ 个互不相同的、取值范围为 $0$ 到 $(m - 1)$ 的整数作为密码。这些整数的输出顺序可以任意。此外，若存在多个解，输出任意一个即可。

In the first example, there is no possible password.

In each of the last three examples, the given integer $n$ equals to the number of possible different passwords for the given integers $m$ and $p$, so if the order of numbers in the output is ignored, the solution is unique as shown above.

在第一个例子中，不存在可能的密码。

在最后三个例子中，给定的整数 $n$ 等于对应整数 $m$ 和 $p$ 下可能的不同密码的数量，因此若忽略输出中数字的顺序，则如上所示，解是唯一的。