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 $P_U<P_V$ for a heaplike permutation chosen uniformly at random.

Definition of probability modulo $998244353$

It can be proved that the sought probability is always rational. Additionally, under the constraints of this problem, when the sought rational number is represented as an irreducible fraction $\\frac{P}{Q}$, it can be proved that $Q \\neq 0 \\pmod{998244353}$. Therefore, there is a unique integer $R$ such that $R \\times Q \\equiv P \\pmod{998244353}$ and $0 \\leq R \\lt 998244353$. Print this $R$.

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.

Sample Input 1

2 1 1

Sample Output 1

499122177

There are two heaplike permutations: $P=(1,2,3),(1,3,2)$. The probability that $P_2<P_3$ is $1/2$.

Sample Input 2

3 1 2

Sample Output 2

124780545

Sample Input 3

4 3 2

Sample Output 3

260479386

Sample Input 4

2022 12 25

Sample Output 4

741532295