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 $998244353$.

What is bitwise XOR? The bitwise $\\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \\oplus B$, is defined as follows.

• When $A \\oplus B$ is written in binary, the $k$-th lowest bit ($k \\geq 0$) is $1$ if exactly one of the $k$-th lowest bits of $A$ and $B$ is $1$, and $0$ otherwise.

For instance, $3 \\oplus 5 = 6$ (in binary: $011 \\oplus 101 = 110$).

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.

Sample Input 1

2 2

Sample Output 1

5

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

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

Sample Input 2

2022 1119

Sample Output 2

293184537

Sample Input 3

200000 10000000

Sample Output 3

383948354