Even Degrees

AtCoder

IDagc035_b

Time2000ms

Memory256MB

Difficulty—

You are given a simple connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$\-th edge connects Vertex $A_i$ and Vertex $B_i$. Takahashi will assign one of the two possible directions to each of the edges in the graph to make a directed graph. Determine if it is possible to make a directed graph with an even number of edges going out from every vertex. If the answer is yes, construct one such graph. ## Constraints * $2 \leq N \leq 10^5$ * $N-1 \leq M \leq 10^5$ * $1 \leq A_i,B_i \leq N (1\leq i\leq M)$ * The given graph is simple and connected. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $:$ $A_M$ $B_M$ [samples] ## Notes An undirected graph is said to be simple when it contains no self-loops or multiple edges.

Samples

Input #1

Output #1

1 2
1 4
3 2
3 4

After this assignment of directions, Vertex $1$ and $3$ will each have two outgoing edges, and Vertex $2$ and $4$ will each have zero outgoing edges.

Input #2

Output #2

\-1

API Response (JSON)

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  "problem": {
    "name": "Even Degrees",
    "description": {
      "content": "You are given a simple connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$. Takahashi will ass",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc035_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a simple connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$. Takahashi will ass...",
      "is_translate": false,
      "language": "English"
    }
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Full JSON Raw Segments