Problem Statement

There are $N coins numbered 1, 2, \ldots, N$ arranged in a row.
Initially, all coins face up.
Snuke chooses a permutation p of $(1,\ldots,N)$ with equal probability, and do N operations.
The i-th operation does the following.

• If the coin numbered i faces down, do nothing.
• If the coin numbered i faces up, turn that coin over and then turn over the coin numbered p_i.

After the N operations, Snuke will receive W^k yen (Japanese currency) from his mother, where k is the number of coins facing up.
Find the expected value of the amount Snuke will get, multiplied by N! (it can be proved that this is an integer), modulo 998244353.

Input

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

Output

Print the expected value of the amount Snuke will get, multiplied by N!, modulo 998244353.

Constraints

• All values in input are integers.
• $1 \leq N \leq 2 \times 10^5$
• $1 \leq W < 998244353$

Sample Input 1

4 2

Sample Output 1

90

• When p=(1,4,2,3), the operations go as follows.
• In the 1-st operation, the coin numbered 1 faces down, and then the coin numbered 1 faces up.
• In the 2-nd operation, the coin numbered 2 faces down, and then the coin numbered 4 faces down.
• In the 3-rd operation, the coin numbered 3 faces down, and then the coin numbered 2 faces up.

• In the 4-th operation, nothing is done.

• In the end, two coins face up, so he receives 4 yen.

Sample Input 2

2 100

Sample Output 2

10001

Sample Input 3

200000 12345

Sample Output 3

541410753

• Be sure to find the value modulo 998244353.

见题面 Input 部分

见题面 Output 部分