Problem Statement

Takahashi has $A$ kinds of level-$1$ gems, and $10^{10^{100}}$ gems of each of those kinds. For an integer $n$ greater than or equal to $2$, he can put $n$ gems that satisfy all of the following conditions into a cauldron to generate a level-$n$ gem in return.

• No two gems are of the same kind.
• Every gem's level is less than $n$.
• For every integer $x$ greater than or equal to $2$, there is at most one level-$x$ gem.

Find the number of kinds of level-$N$ gems that Takahashi can obtain, modulo $998244353$.

Here, two level-$2$ or higher gems are considered to be of the same kind if and only if they are generated from the same set of gems.

• Two sets of gems are distinguished if and only if there is a gem in one of those sets such that the other set does not contain a gem of the same kind.

Any level-$1$ gem and any level-$2$ or higher gem are of different kinds.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq A \leq 10^9$
• $N$ and $A$ are integers.

Input

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

N A

Output

Print the answer.