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.