\(4^{th}\) round, January \(19^{th}\), 2013

In the faraway city of Xanadu, a flu epidemic has broken out, caused by a strain known as hairy flu.
There are M people living in the city, each resident having a unique personal ID number from the
range of 0 to M – 1, inclusive. Infection with this strain lasts exactly one day, and a person can catch it
multiple times per season (since it mutates too quickly for lasting immunity).
On the first day of the epidemic, the flu was brought from another faraway country by a group of
residents nicknamed “in\(it-pa\)tients”, whose ID numbers are known. The flu's spread is based on them.
Each following day, a resident with ID number p will catch the flu iff there exists a resident with ID a
who was infected the previous day, as well as an in\(it-pa\)tient with ID b, such that:
(\(a * b\)) mod \(M = p\).
The numbers a and b need not be distinct. For example, consider a case where there are 101 people in
the town, and the in\(it-pa\)tients are 5 and 50. On the first day, the in\(it-pa\)tients are infected by definition.
On the second day, the residents infected are 25, 48 (250 mod 101), and 76 (2500 mod 101). On the
third day, one of the infected patients is 77, since (\(48 * 50\)) mod \(101 = 77\).
Who will catch the flu on the \(K-th\) day?

The first line of input contains three positive integers, K, M, and N (\(1 \le K \le 10^{18}\), \(3 \le M \le 1500\), N <
M).
The second line of input contains N spa\(ce-se\)parated nonnegative integers, the personal ID numbers of
residents who were infected on the first day (the in\(it-pa\)tients). These numbers are unique, increasing,
and do not exceed \(M - 1\).

The first and only line of output must contain the personal ID numbers of residents infected with flu
on the \(K-th\) day, given spa\(ce-se\)parated and in increasing order.

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출처 COCI 2012/2013 Contest 4