Problem Statement

PCT-kun created the following problem.

Increasing Problem
You are given a length-N sequence of $non-negative integers A_1,A_2,\dots,A_N.$ You can perform the following operation any number of times (possibly zero).

• Choose an integer i such that $1 \le i \le N$, and increase or decrease A_i by 1.

Your goal is to make A non-decreasing. Find the minimum number of operations required to achieve this goal.

Thinking that this problem is too easy to be placed at the end of the contest, PCT-kun has revised it as follows.

Many Increasing Problems
There are M^N integer sequences A of length N where all elements are between 1 and M, inclusive. Find the sum of the answers to Increasing Problem for all those sequences, modulo 998244353.

Solve Many Increasing Problems.

Input

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

Output

Print the answer to Many Increasing Problems.

Constraints

• $1 \le N,M \le 10^5$

Sample Input 1

2 2

Sample Output 1

1

Let us solve Increasing Problem for all sequences of length 2 where all elements are between 1 and 2, inclusive.

• For A=(1,1), the answer is 0.
• For A=(1,2), the answer is 0.
• For A=(2,1), the answer is 1.
• For A=(2,2), the answer is 0.

Therefore, the final answer is 0+0+1+0=1.

Sample Input 2

6 4

Sample Output 2

14668

Sample Input 3

163 702

Sample Output 3

20728656

Sample Input 4

98765 99887

Sample Output 4

103564942

见题面 Input 部分

见题面 Output 部分