Problem Statement

Given are integers N and M.
Find the number of integer sequences $a=(a_1,a_2,\cdots,a_N)$ that can be generated as follows, modulo 998244353.

• Provide an undirected connected graph G with N vertices and M edges.
  Here, G may not contain self-loops, but may contain multi-edges.
• Perform DFS on G and let a_i be the degree of the i-th vertex to be visited.
  More accurately, execute the pseudo-code below to get a.

a = empty array

dfs(v):
visited[v]=True
a.append(degree[v])
for u in g[v]:
if not visited[u]:
dfs(u)

dfs(arbitrary root)

Here, the variable g represents the graph G as an adjacency list, where g[v] is the list of vertices adjacent to the vertex v in arbitrary order.
For example, when N=4,M=5, it is possible to generate a=(2,4,1,3), by providing the graph G as follows.

Here, the numbers written on vertices represent the order they are visited in the DFS. (The DFS starts at the vertex labeled 1.)
The orange arrows show the transitions in the DFS, and the numbers next to them represent the order the edges are traversed.

Input

Input is given from Standard Input in the following format:
N M

Output

Print the answer.

Constraints

• $2 \leq N \leq M \leq 10^6$
• All values in input are integers.

Sample Input 1

2 2

Sample Output 1

1

The only possible result is a=(2,2).
Note that G may have multi-edges.

Sample Input 2

3 4

Sample Output 2

9

Sample Input 3

10 20

Sample Output 3

186225754

Sample Input 4

100000 1000000

Sample Output 4

191021899

见题面 Input 部分

见题面 Output 部分