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.
• $A_{i} \equiv aA_{i-1}\pmod{P}$
• $A_{i-1} \equiv aA_{i}\pmod{P}$
• $A_{i} \equiv bA_{i-1}\pmod{P}$
• $A_{i-1} \equiv bA_{i}\pmod{P}$

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分