Source

This problem is adapted from Long Long OJ. All rights reserved.

Problem Background

In the distant Gensokyo, an outbreak of idiocy flu has occurred.

Problem Description

There are $M$ residents living in Gensokyo, each with a unique and distinct personal ID number ranging from $0$ to $M-1$.

On the first day, $N$ people are infected, and we know their IDs. In the subsequent days, a person with ID $p$ will be infected on a certain day if and only if:

1. Some resident $a$ was infected on the previous day;
2. Some resident $b$ was infected on the first day (note: $a$ and $b$ can be the same here);
3. $a$ and $b$ satisfy the condition: $a \times b \equiv p \pmod M$.

Each resident can be infected repeatedly! Please write a program to find out which people will be infected on the $K$-th day.

Input Format

The first line contains three non-negative integers $K, M, NK, M, N\ (1 \le K \le 10^{18}, 3 \le M \le 1500, 0 \le N \le M - 1)$.

The second line contains $N$ distinct non-negative integers (in the range $[0, M - 1]$) representing the ID's of people infected on the first day.

Output Format

Output a line with several non-negative integers (in ascending order), representing the ID's of people infected on the $K$-th day.

Samples

1 100 3
1 2 3

1 2 3

2 100 3
1 2 3

1 2 3 4 6 9

3 101 2
5 50

24 38 63 77