Problem Statement

Consider a directed graph G with N vertices numbered 1 to N that satisfies all of the following conditions.

• G is a tournament. In other words, G has no multi-edges or self-loops, and for any two vertices u,v of G, exactly one of the edges $u \rightarrow v$ and $v \rightarrow u$ exists.

• Among the edges of G, exactly M are directed from a vertex with a smaller number to a vertex with a larger number.

Find the total number of strongly connected components over all such directed graphs G, modulo 998244353.

Input

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

Output

Print the answer.

Constraints

• $1 \le N \le 30$
• $0 \le M \le \frac{N(N-1)}{2}$

Sample Input 1

3 1

Sample Output 1

7

Below are the three directed graphs G that satisfy the conditions. The numbers of their strongly connected components are 3,1,3 from left to right, so the answer is 7.

Sample Input 2

6 2

Sample Output 2

300

Sample Input 3

25 156

Sample Output 3

902739687

见题面 Input 部分

见题面 Output 部分