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.