Score : $800$ points

Problem Statement

Consider a permutation $P=(P_1,P_2,\cdots,P_{2^N-1})$ of $(1,2,\cdots,2^N-1)$. $P$ is said to be heaplike if and only if all of the following conditions are satisfied.

• $P_i < P_{2i}$ ($1 \leq i \leq 2^{N-1}-1$)
• $P_i < P_{2i+1}$ ($1 \leq i \leq 2^{N-1}-1$)

You are given integers $A$ and $B$. Let $U=2^A$ and $V=2^{B+1}-1$.

Find the probability, modulo $998244353$, that $P_U for a heaplike permutation chosen uniformly at random.

Constraints

• $2 \leq N \leq 5000$
• $1 \leq A,B \leq N-1$
• All numbers in the input are integers.

Input

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

$N$ $A$ $B$

Output

Print the answer.

2 1 1

499122177

There are two heaplike permutations: $P=(1,2,3),(1,3,2)$. The probability that $P_2 is $1/2$.

3 1 2

124780545

4 3 2

260479386

2022 12 25

741532295