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 $p_1, p_2, p_3, \dots, p_k$.
  

Input

Input is given from Standard Input in the following format:
N M

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分