201183: [AtCoder]ARC118 D - Hamiltonian Cycle

Problem Statement

Given are a prime number $P$ and positive integers $a$ and $b$. Determine whether there is a sequence of $P$ integers, $A = (A_1, A_2, \ldots, A_P)$, satisfying all of the conditions below, and print one such sequence if it exists.

• $1\leq A_i\leq P - 1$.
• $A_1 = A_P = 1$.
• $(A_1, A_2, \ldots, A_{P-1})$ is a permutation of $(1, 2, \ldots, P-1)$.
• For every $2\leq i\leq P$, at least one of the following holds.
  • $A_{i} \equiv aA_{i-1}\pmod{P}$
  • $A_{i-1} \equiv aA_{i}\pmod{P}$
  • $A_{i} \equiv bA_{i-1}\pmod{P}$
  • $A_{i-1} \equiv bA_{i}\pmod{P}$

Constraints

• $2\leq P\leq 10^5$
• $P$ is a prime.
• $1\leq a, b \leq P - 1$

Input

Input is given from Standard Input in the following format:

$P$ $a$ $b$

Output

If there is an integer sequence $A$ satisfying the conditions, print Yes; otherwise, print No. In the case of Yes, print the elements in your sequence $A$ satisfying the requirement in the next line, with spaces in between.

$A_1$ $A_2$ $\ldots$ $A_P$

If multiple sequences satisfy the requirement, any of them will be accepted.

Sample Input 1

13 4 5

Sample Output 1

Yes
1 5 11 3 12 9 7 4 6 8 2 10 1

This sequence satisfies the conditions, since we have the following modulo $P = 13$:

• $A_2\equiv 5A_1$
• $A_2\equiv 4A_3$
• $\vdots$
• $A_{13}\equiv 4A_{12}$

Sample Input 2

13 1 2

Sample Output 2

Yes
1 2 4 8 3 6 12 11 9 5 10 7 1

Sample Input 3

13 9 3

Sample Output 3

No

Sample Input 4

13 1 1

Sample Output 4

No