Problem Statement

There are $N$ white balls. First, you paint each ball red or blue.

Then, you place these $N$ red or blue painted balls in one of $M$ distinguishable boxes.

Let $a_i$ and $b_i$ be the number of red and blue balls in the $i$-th box, respectively.

Find the sum, modulo $998244353$, of $\prod_{1\leq i \le M}|a_i-b_i|$ over all ways to place the balls.

Here, two ways of placing balls are different if and only if at least one of $a_i$ and $b_i$ is different for some $i$.

Particularly, balls are not distinguished from each other.

Constraints

• $1 \le N,M \le 10^7$
• All input values are integers.

Input

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

N M

Output

Output the answer.