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.

Input

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

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分