Pure

AtCoder

IDabc142_f

Time2000ms

Memory256MB

Difficulty—

Given is a directed graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$\-th edge is directed from Vertex $A_i$ to Vertex $B_i$. It is guaranteed that the graph contains no self-loops or multiple edges. Determine whether there exists an induced subgraph (see Notes) of $G$ such that the in-degree and out-degree of every vertex are both $1$. If the answer is yes, show one such subgraph. Here the null graph is not considered as a subgraph. ## Constraints * $1 \leq N \leq 1000$ * $0 \leq M \leq 2000$ * $1 \leq A_i,B_i \leq N$ * $A_i \neq B_i$ * All pairs $(A_i, B_i)$ are distinct. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $:$ $A_M$ $B_M$ [samples] ## Notes For a directed graph $G = (V, E)$, we call a directed graph $G' = (V', E')$ satisfying the following conditions an induced subgraph of $G$: * $V'$ is a (non-empty) subset of $V$. * $E'$ is the set of all the edges in $E$ that have both endpoints in $V'$.

Samples

Input #1

Output #1

3
1
2
4

The induced subgraph of $G$ whose vertex set is ${1, 2, 4}$ has the edge set ${(1, 2), (2, 4), (4, 1)}$. The in-degree and out-degree of every vertex in this graph are both $1$.

Input #2

Output #2

\-1

There is no induced subgraph of $G$ that satisfies the condition.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Pure",
    "description": {
      "content": "Given is a directed graph $G$ with $N$ vertices and $M$ edges.   The vertices are numbered $1$ to $N$, and the $i$\\-th edge is directed from Vertex $A_i$ to Vertex $B_i$.   It is guaranteed that the g",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc142_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a directed graph $G$ with $N$ vertices and $M$ edges.  \nThe vertices are numbered $1$ to $N$, and the $i$\\-th edge is directed from Vertex $A_i$ to Vertex $B_i$.  \nIt is guaranteed that the g...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments