Problem Statement

tubuann is a mysterious creature living in the world of non-negative integers.
For tubuann's birthday, you have decided to give a set $S$ of size $N$ consisting of non-negative integers less than $2^M$.
tubuann is initially at $0$ and can perform the following action any number of times, possibly $0$ times.

• Let $a$ be the current location.
• Choose one $s \in S$ and move to $a \oplus s$.

• The number of locations tubuann can move to when $S$ is chosen so as to maximize the number of locations tubuann can move to.
  That is, $\max |f(S)|$. Let this value be $A$.
• The number of sets $S$ that maximize the number of locations tubuann can move to.
  That is, $|\{S\mid |f(S)|=A\}|$.
• The number of sets of locations tubuann can move to when $S$ maximizes the number of locations tubuann can move to.
  That is, $|\{f(S)\mid |f(S)|=A\}|$.

Input

$N\ M$

$1 \leq N \leq M \leq 2 \times 10^5$
All inputs are integers.

Output

The number of locations tubuann can move to when $S$ is chosen so as to maximize the number of locations tubuann can move to.
The number of sets $S$ that maximize the number of locations tubuann can move to.
The number of sets of locations tubuann can move to when $S$ maximizes the number of locations tubuann can move to.
Output each of these three values modulo $998244353$ in this order on one line, separated by spaces.

Sample

1 1

2 1 1

1 2

2 3 3

7 100

128 275646563 10439943