Problem11265--[yosupo] Graph - Chromatic Polynomial

11265: [yosupo] Graph - Chromatic Polynomial

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

Given an undirected graph $G$ with $N$ vertices and $M$ edges. The $i$-th edge is $\lbrace u_i, v_i\rbrace$. 

Calculate the chromatic polynomial $P(G,x)=p_0+p_1+\cdots+p_Nx^N$ modulo $998244353$.

Input

$N$ $M$
$u_0$ $v_0$
$u_1$ $v_1$
:
$u_{M - 1}$ $v_{M - 1}$

Output

$p_0$ $p_1$ $\cdots$ $p_N$

Constraints

- $1 \leq N \leq 20$
- $0 \leq M \leq 500$
- $0 \leq u_i, v_i < N$

Sample 1 Input

5 7
0 1
0 2
0 4
1 3
2 3
2 4
3 4

Sample 1 Output

0 10 998244330 19 998244346 1

Sample 2 Input

20 0

Sample 2 Output

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

Sample 3 Input

3 1
2 2

Sample 3 Output

0 0 0 0

2 5
0 1
1 0
0 1
0 1
1 0

0 998244352 1

HINT

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