Hamiltonian Cycle

AtCoder

IDarc118_d

Time2000ms

Memory256MB

Difficulty—

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: $P$ $a$ $b$ [samples]

Samples

Input #1

13 4 5

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 $P = 13$:

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

Input #2

13 1 2

Output #2

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

Input #3

13 9 3

Output #3

No

Input #4

13 1 1

Output #4

No

API Response (JSON)

{
  "problem": {
    "name": "Hamiltonian Cycle",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc118_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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