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.

Input

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

Output

Print the answer.

Constraints

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

Sample Input 1

3 3

Sample Output 1

10

Here are ten ways to obtain a level-3 gem.

• Put three kinds of level-1 gems into the cauldron.

• Takahashi has three kinds of level-1 gems, so there is one way to choose three kinds of level-1 gems. Thus, he can obtain one kind of level-3 gem in this way.

• Put one kind of level-2 gem and two kinds of level-1 gems into the cauldron.

• A level-2 gem can be obtained by putting two kinds of level-1 gems into the cauldron.

• Takahashi has three kinds of level-1 gems, so there are three ways to choose two kinds of level-1 gems. Thus, three kinds of level-2 gems are available here.

• There are three kinds of level-2 gems, and three ways to choose two kinds of level-1 gems, so he can obtain $3 \times 3 = 9$ kinds of level-3 gems in this way.

Sample Input 2

1 100

Sample Output 2

100

Sample Input 3

200000 1000000000

Sample Output 3

797585162

见题面 Input 部分

见题面 Output 部分