Problem Statement

PCT made the following problem.

Xor Optimization Problem

You are given a sequence of non-negative integers of length $N$: $A_1,A_2,...,A_N$. When it is allowed to choose any number of elements in $A$, what is the maximum possible $\\mathrm{XOR}$ of the chosen values?

Nyaan thought it was too easy and revised it to the following.

Many Xor Optimization Problems

There are $2^{NM}$ sequences of length $N$ consisting of integers between $0$ and $2^M-1$. Find the sum, modulo $998244353$, of the answers to Xor Optimization Problem for all those sequences.

Solve Many Xor Optimization Problems.

What is bitwise $\\mathrm{XOR}$?

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 base two, the digit in the $2^k$'s place ($k \\geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise.

For example, we have $3 \\oplus 5 = 6$ (in base two: $011 \\oplus 101 = 110$).
Generally, the bitwise $\\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \\dots, p_k$ is defined as $(\\dots ((p_1 \\oplus p_2) \\oplus p_3) \\oplus \\dots \\oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \\dots, p_k$.

Constraints

• $1 \\le N,M \\le 250000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the answer.

Sample Input 1

2 1

Sample Output 1

3

We are to solve Xor Optimization Problem for all sequences of length $2$ consisting of integers between $0$ and $1$.

• The answer for $A=(0,0)$ is $0$.
• The answer for $A=(0,1)$ is $1$.
• The answer for $A=(1,0)$ is $1$.
• The answer for $A=(1,1)$ is $1$.

Thus, the final answer is $0+1+1+1=3$.

Sample Input 2

3 4

Sample Output 2

52290

Sample Input 3

1234 5678

Sample Output 3

495502261