Problem Statement

You are given positive integers $N,K$. A sequence of length $N$ is called a good sequence if it satisfies the following conditions.

• For every integer $i$ satisfying $1 \le i \le N $, $ S_i \in \lbrace 0,1 \rbrace$
• $\displaystyle \sum_{i=1}^N S_i \equiv 0 \ (\mathrm{mod}\ 2)$

For a good sequence $S$, let $f(S)$ be the minimum number of operations required to make all elements of $S$ equal to $0$ by performing the following operation $0$ or more times. (If $S$ is a good sequence, $f(S)$ is a finite value.)

• Choose one integer $i$ satisfying $1 \le i \le N-1$, replace $S_i$ with $1-S_i$, and replace $S_{i+1}$ with $1-S_{i+1}$.

There are $2^{N-1}$ good sequences $S$. Compute $f(S)$$^K$ for all of them, and find the sum of these values modulo $998244353$.

Input

$N$ $K$

Output

Print the sum of $f(S)^K$ modulo $998244353$.

Sample

3 2

6

10 3

62208

200000 2

829773566