Problem Statement

$2^N$ distinguishable people will play the AtCoder Janken Train. Of the $2^N$ people, $M$ are "cool-colored" and the remaining $2^N - M$ are "warm-colored".

Find the total number of possible arrangements of the final line after the AtCoder Janken Train has finished, modulo $998244353$.

Here, the AtCoder Janken Train is defined as the following procedure.

• First, the $2^N$ people form $2^N$ lines, each consisting of $1$ person.
• If $N \ge 1$, then for $t = 0, 1, \dots, N - 1$, in this order, perform the following operation for the integer $t$.
  1. Let $K = 2^{N-t}$ be the current number of lines.
  2. Partition these $K$ lines into $\dfrac{K}{2}$ pairs in an arbitrary way.
  3. For each of the resulting $\dfrac{K}{2}$ pairs $(L_A, L_B)$, perform the following operation to make $\dfrac{K}{2}$ new lines.
     • Let $h_A$ be the person at the front of $L_A$, and $h_B$ be the person at the front of $L_B$.
     • $h_A$ and $h_B$ play janken (rock-paper-scissors) until one of them wins.
     • If $h_A$ is "cool-colored" and $h_B$ is "warm-colored", attach $L_A$ behind $L_B$ to make a new line.
     • If $h_A$ is "warm-colored" and $h_B$ is "cool-colored", attach $L_B$ behind $L_A$ to make a new line.
     • Otherwise, if $h_A$ won the janken, attach $L_B$ behind $L_A$, and if $h_B$ won, attach $L_A$ behind $L_B$, to make a new line.

After all the operations are finished, there is exactly $1$ line.

Constraints

• $0 \le N \le 18$
• $0 \le M \le 2^N$
• $N, M$ are integers.

Input

The input is given from standard input in the following format.

$N$ $M$

Output

Output the answer.

Sample

2 2

8

3 0

40320

18 192109

659921266