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.

Input

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

Output

Print the answer.

Constraints

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

Sample Input 1

2 3

Sample Output 1

24

Among all possible brilliant sequences, the following 6 have positive scores.

• S_1={1,2},S_2={1,2,3}
• S_1={1,3},S_2={1,2,3}
• S_1={2,3},S_2={1,2,3}
• S_1={1,2,3},S_2={1,2}
• S_1={1,2,3},S_2={1,3}
• S_1={1,2,3},S_2={2,3}

All of them have a score of 4, so the sum of them is 24.

Sample Input 2

12 34

Sample Output 2

786334067

见题面 Input 部分

见题面 Output 部分