Find 4-cycle

AtCoder

IDabc260_f

Time2000ms

Memory256MB

Difficulty—

We have a simple undirected graph $G$ with $(S+T)$ vertices and $M$ edges. The vertices are numbered $1$ through $(S+T)$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertices $u_i$ and $v_i$. Here, vertex sets $V_1 = \lbrace 1, 2,\dots, S\rbrace$ and $V_2 = \lbrace S+1, S+2, \dots, S+T \rbrace$ are both independent sets. A cycle of length $4$ is called a 4-cycle. If $G$ contains a 4-cycle, choose any of them and print the vertices in the cycle. You may print the vertices in any order. If $G$ does not contain a 4-cycle, print `-1`. What is an independent set? An independent set of a graph $G$ is a set $V'$ of some of the vertices in $G$ such that no two vertices of $V'$ have an edge between them. ## Constraints * $2 \leq S \leq 3 \times 10^5$ * $2 \leq T \leq 3000$ * $4 \leq M \leq \min(S \times T,3 \times 10^5)$ * $1 \leq u_i \leq S$ * $S + 1 \leq v_i \leq S + T$ * If $i \neq j$, then $(u_i, v_i) \neq (u_j, v_j)$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $S$ $T$ $M$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_M$ $v_M$ [samples]

Samples

Input #1

Output #1

1 2 4 5

There are edges between Vertices $1$ and $4$, $4$ and $2$, $2$ and $5$, and $5$ and $1$, so Vertices $1$, $2$, $4$, and $5$ form a 4-cycle. Thus, $1$, $2$, $4$, and $5$ should be printed.  
The vertices may be printed in any order. Besides the Sample Output, `2 5 1 4` is also considered correct, for example.

Input #2

Output #2

\-1

Some inputs may give $G$ without a 4-cycle.

Input #3

Output #3

1 7 2 9

API Response (JSON)

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    "name": "Find 4-cycle",
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      "content": "We have a simple undirected graph $G$ with $(S+T)$ vertices and $M$ edges. The vertices are numbered $1$ through $(S+T)$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertices $u_i$ a",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc260_f"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a simple undirected graph $G$ with $(S+T)$ vertices and $M$ edges. The vertices are numbered $1$ through $(S+T)$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertices $u_i$ a...",
      "is_translate": false,
      "language": "English"
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  ]
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