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D - Hamiltonian Cycle /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

• 1\leq A_i\leq P - 1
• A_1 = A_P = 1
• (A_1, A_2, \ldots, A_{P-1}) は、(1, 2, \ldots, P-1) を並べ替えたものである
• 任意の 2\leq i\leq P に対して、次のうち少なくともひとつが成り立つ：
• 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}

制約

• 2\leq P\leq 10^5
• P は素数
• 1\leq a, b \leq P - 1

入力

P a b


出力

A_1 A_2 \ldots A_P


入力例 1

13 4 5


出力例 1

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


P = 13 を法として、

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

が成り立ち、この整数列は条件を満たすことが確認できます。

入力例 2

13 1 2


出力例 2

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


入力例 3

13 9 3


出力例 3

No


入力例 4

13 1 1


出力例 4

No


Score : 700 points

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