Problem Statement

Consider a sequence of integer sets of length $N$: $S=(S_1,S_2,\dots,S_N)$. We call a sequence brilliant if it satisfies all of the following conditions:

• $S_i$ is a (possibly empty) integer set, and its elements are in the range $[1,M]$. $(1 \le i \le N)$
• The number of integers that is included in exactly one of $S_i$ and $S_{i+1}$ is $1$. $(1 \le i \le N-1)$

We define the score of a brilliant sequence $S$ as $\displaystyle \prod_{i=1}^{M}$ $($ the number of sets among $S_1,S_2,\dots,S_N$ that include $i$.$)$.

Find, modulo $998244353$, the sum of the scores of all possible brilliant sequences.

Constraints

• $1 \le N,M \le 2 \times 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the answer.