Score: $1200$ points

问题陈述

黑板上写着一组正整数。最初，黑板上写着集合 ( S={1,2,\dots,A,A+1,A+2,\dots,A+B} )。

高桥想要执行以下操作 ( N-1 ) 次，以便在黑板上得到 ( N ) 个集合：

• 从黑板上写的整数集合中，选择一个集合 ( S_0 )，该集合至少包含一个不超过 ( A ) 的元素，并且至少包含一个不少于 ( A+1 ) 的元素。从选定的集合 ( S_0 ) 中，选择一个不超过 ( A ) 的元素 ( a ) 和一个不少于 ( A+1 ) 的元素 ( b )。从黑板上擦掉集合 ( S_0 ) 并写下两个集合 ( S_1 ) 和 ( S_2 )，这两个集合由他选择，并且满足以下所有条件：
  • ( S_1 ) 和 ( S_2 ) 的并集是 ( S_0 )，并且它们没有共同元素。
  • ( a \in S_1, b \in S_2 )

找出执行一系列操作的可能方式的数量，对 ( 998244353 ) 取模。

在这里，当存在 ( i\ (1 \leq i \leq N-1) ) 使得一个系列中 ( i ) 次操作选择的 ( S_0 )，( a )，( b )，( S_1 ) 或 ( S_2 ) 与另一个系列中的不同，则认为两个操作系列是不同的。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There is a blackboard with a set of positive integers written on it. Initially, the set $S=\lbrace 1,2,\dots,A,A+1,A+2,\dots,A+B\rbrace$ is written on the blackboard.

Takahashi wants to perform the following operation $N-1$ times to have $N$ sets on the blackboard:

• From the sets of integers written on the blackboard, choose a set $S_0$ that contains at least one element not greater than $A$ and at least one element not less than $A+1$. From the chosen set $S_0$, choose one element $a$ not greater than $A$ and one element $b$ not less than $A+1$. Erase the set $S_0$ from the blackboard and write two sets $S_1$ and $S_2$ of his choice that satisfy all of the following conditions:
  • The union of $S_1$ and $S_2$ is $S_0$, and they have no common elements.
  • $a \in S_1, b \in S_2$

Find the number of possible ways to perform the series of operations, modulo $998244353$.

Here, two series of operations are distinguished when there is an $i\ (1 \leq i \leq N-1)$ such that $S_0$, $a$, $b$, $S_1$, or $S_2$ chosen in the $i$-th operation of one series is different from that of the other series.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A,B \leq 2 \times 10^5$
• $N \leq A+B$
• All input values are integers.

Input

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

$N$ $A$ $B$

Output

Print the answer.

Sample Input 1

3 2 4

Sample Output 1

1728

One possible series of operations is as follows:

• Choose $S_0=\lbrace 1,2,3,4,5,6\rbrace$, let $a=2$ and $b=5$, and let $S_1 =\lbrace 1,2,3,6\rbrace$ and $S_2=\lbrace 4,5\rbrace$. There are now two sets of integers written on the blackboard: $\lbrace 1,2,3,6\rbrace$ and $\lbrace 4,5\rbrace$.
• Choose $S_0=\lbrace 1,2,3,6\rbrace$, let $a=1$ and $b=3$, and let $S_1 = \lbrace1,2\rbrace$ and $S_2=\lbrace 3,6\rbrace$. There are now three sets of integers written on the blackboard: $\lbrace 1,2\rbrace$, $\lbrace 3,6\rbrace$, and $\lbrace 4,5\rbrace$.

Sample Input 2

4 1 3

Sample Output 2

6

If we let $a=1$ and $b=2$ and let $S_1 = \lbrace 1\rbrace$ and $S_2 = \lbrace 2,3,4\rbrace$ in the first operation, we can no longer perform the second and subsequent operations.

Do not count these cases where we cannot complete $N-1$ operations.

Sample Input 3

5 6 6

Sample Output 3

84486693

Sample Input 4

173173 173173 173173

Sample Output 4

446948086