Problem Statement

There is a tree with $NM+1$ vertices numbered $0$ to $NM$. The $i$-th edge ($1 \le i \le NM$) connects vertices $i$ and $\max(i-N,0)$.

Initially, vertex $i$ is colored with color $i \bmod N$. You can perform the following operation zero or more times:

• Choose two vertices $u$ and $v$ connected by an edge. Repaint the color of vertex $u$ with that of vertex $v$.

Find the number, modulo $998244353$, of possible trees after the operations. Two trees are distinguished if and only if some vertex has different colors.

Constraints

• $1 \le N, M \le 2 \times 10^5$

Input

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

N M

Output

Print the answer.