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 $998244353$.

Constraints

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

Input

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

$N$ $M$

Output

Print the answer.

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