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.