Problem Statement

You are given a prime number $P$, which you don't like.

Let's call an array of integers $A_1, A_2, \\dots, A_N$ good, if it is possible to reorder the elements in such a way that no prefix sum is divisible by $P$ (that is, there is no $i$ with $1 \\le i \\le N$ and $A_1 + A_2 + \\dots + A_i \\equiv 0 \\bmod P$ after the reordering).

Consider all $(P-1)^N$ arrays of length $N$ with elements from $1$ to $P-1$. How many of them are good?

As this number can be very big, output it modulo $998244353$.

Constraints

• $1 \\le N \\le 5000$
• $2 \\le P \\le 10^8$
• $P$ is a prime.

Input

Input is given from Standard Input in the following format:

$N$ $P$

Output

Output the number of good arrays modulo $998244353$.

Sample Input 1

2 5

Sample Output 1

12

There are $12$ good arrays: \[1, 1\], \[1, 2\], \[1, 3\], \[2, 1\], \[2, 2\], \[2, 4\], \[3, 1\], \[3, 3\], \[3, 4\], \[4, 2\], \[4, 3\], \[4, 4\].

Sample Input 2

4 3

Sample Output 2

8

There are $8$ good arrays: \[1, 1, 1, 2\], \[1, 1, 2, 1\], \[1, 2, 1, 1\], \[2, 1, 1, 1\], $\[2, 2, 2, 1$], \[2, 2, 1, 2\], \[2, 1, 2, 2\], \[1, 2, 2, 2\].

Sample Input 3

5000 99999989

Sample Output 3

51699346

Sample Input 4

2021 307

Sample Output 4

644635349