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 $998244353$.

Constraints

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

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 $998244353$.