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