{"raw_statement":[{"iden":"problem statement","content":"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.\n\n*   $P_i < P_{2i}$ ($1 \\leq i \\leq 2^{N-1}-1$)\n*   $P_i < P_{2i+1}$ ($1 \\leq i \\leq 2^{N-1}-1$)\n\nYou are given integers $A$ and $B$. Let $U=2^A$ and $V=2^{B+1}-1$.\nFind the probability, modulo $998244353$, that $P_U<P_V$ for a heaplike permutation chosen uniformly at random.\n\nDefinition of probability modulo $998244353$\n\nIt 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 $R$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 5000$\n*   $1 \\leq A,B \\leq N-1$\n*   All numbers in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $A$ $B$"},{"iden":"sample input 1","content":"2 1 1"},{"iden":"sample output 1","content":"499122177\n\nThere are two heaplike permutations: $P=(1,2,3),(1,3,2)$. The probability that $P_2<P_3$ is $1/2$."},{"iden":"sample input 2","content":"3 1 2"},{"iden":"sample output 2","content":"124780545"},{"iden":"sample input 3","content":"4 3 2"},{"iden":"sample output 3","content":"260479386"},{"iden":"sample input 4","content":"2022 12 25"},{"iden":"sample output 4","content":"741532295"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}