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.