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.

Constraints

• $1 \\le N,M \\le 10^5$

Input

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

$N$ $M$

Output

Print the answer to Many Increasing Problems.

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