Connectivity 2

AtCoder

IDabc213_g

Time3000ms

Memory256MB

Difficulty—

Given is a simple undirected graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1,2,\dots,N$, the edges are numbered $1,2,\dots,M$, and Edge $i$ connects Vertex $a_i$ and Vertex $b_i$. Consider removing zero or more edges from $G$ to get a new graph $H$. There are $2^M$ graphs that we can get as $H$. Among them, find the number of such graphs that Vertex $1$ and Vertex $k$ are directly or indirectly connected, for each integer $k$ such that $2 \leq k \leq N$. Since the counts may be enormous, print them modulo $998244353$. ## Constraints * $2 \leq N \leq 17$ * $0 \leq M \leq \frac{N(N-1)}{2}$ * $1 \leq a_i \lt b_i \leq N$ * $(a_i, b_i) \neq (a_j, b_j)$ if $i \neq j$. * 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

3 2
1 2
2 3

Output #1

2
1

We can get the following graphs as $H$.

*   The graph with no edges. Vertex $1$ is disconnected from any other vertex.
*   The graph with only the edge connecting Vertex $1$ and $2$. Vertex $2$ is reachable from Vertex $1$.
*   The graph with only the edge connecting Vertex $2$ and $3$. Vertex $1$ is disconnected from any other vertex.
*   The graph with both edges. Vertex $2$ and $3$ are reachable from Vertex $1$.

Input #2

Output #2

Input #3

2 0

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Connectivity 2",
    "description": {
      "content": "Given is a simple undirected graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1,2,\\dots,N$, the edges are numbered $1,2,\\dots,M$, and Edge $i$ connects Vertex $a_i$ and Vertex $b_",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc213_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a simple undirected graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1,2,\\dots,N$, the edges are numbered $1,2,\\dots,M$, and Edge $i$ connects Vertex $a_i$ and Vertex $b_...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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