Restricted Permutation

AtCoder

IDabc223_d

Time2000ms

Memory256MB

Difficulty—

Among the sequences $P$ that are permutations of $(1, 2, \dots, N)$ and satisfy the condition below, find the lexicographically smallest sequence. * For each $i = 1, \dots, M$, $A_i$ appears earlier than $B_i$ in $P$. If there is no such $P$, print `-1`. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq M \leq 2 \times 10^5$ * $1 \leq A_i, B_i \leq N$ * $A_i \neq B_i$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $\vdots$ $A_M$ $B_M$ [samples]

Samples

Input #1

Output #1

2 1 3 4

The following five permutations $P$ satisfy the condition: $(2, 1, 3, 4), (2, 3, 1, 4), (2, 3, 4, 1), (3, 2, 1, 4), (3, 2, 4, 1)$. The lexicographically smallest among them is $(2, 1, 3, 4)$.

Input #2

Output #2

\-1

No permutations $P$ satisfy the condition.

API Response (JSON)

{
  "problem": {
    "name": "Restricted Permutation",
    "description": {
      "content": "Among the sequences $P$ that are permutations of $(1, 2, \\dots, N)$ and satisfy the condition below, find the lexicographically smallest sequence. *   For each $i = 1, \\dots, M$, $A_i$ appears earlie",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc223_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Among the sequences $P$ that are permutations of $(1, 2, \\dots, N)$ and satisfy the condition below, find the lexicographically smallest sequence.\n\n*   For each $i = 1, \\dots, M$, $A_i$ appears earlie...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments