Score : $600$ points

Problem Statement

A sequence $S$ of non-negative integers is said to be a good sequence if:

• there exists a non-empty (not necessarily contiguous) subsequence $T$ of $S$ such that the bitwise XOR of all elements in $T$ is $1$.

There are an empty sequence $A$, and $2^B$ cards with each of the integers between $0$ and $2^B-1$ written on them. You repeat the following operation until $A$ becomes a good sequence:

• You freely choose a card and append the integer written on it to the tail of $A$. Then, you eat the card. (Once eaten, the card cannot be chosen anymore.)

How many sequences of length $N$ can be the final $A$ after the operations? Find the count modulo $998244353$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq B \leq 10^7$
• $N \leq 2^B$
• $N$ and $B$ are integers.

Input

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

$N$ $B$

Output

Print the answer.

2 2

5

The following five sequences of length $2$ can be the final $A$ after the operations.

• $(0, 1)$
• $(2, 1)$
• $(2, 3)$
• $(3, 1)$
• $(3, 2)$

2022 1119

293184537

200000 10000000

383948354