{"raw_statement":[{"iden":"problem statement","content":"You are given integers $N,\\ A$ and $B$. Determine if there exists a permutation $(P_0,\\ P_1,\\ ...\\ P_{2^N-1})$ of $(0,\\ 1,\\ ...\\ 2^N-1)$ that satisfies all of the following conditions, and create one such permutation if it exists.\n\n*   $P_0=A$\n*   $P_{2^N-1}=B$\n*   For all $0 \\leq i < 2^N-1$, the binary representations of $P_i$ and $P_{i+1}$ differ by exactly one bit."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 17$\n*   $0 \\leq A \\leq 2^N-1$\n*   $0 \\leq B \\leq 2^N-1$\n*   $A \\neq B$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $A$ $B$"},{"iden":"sample input 1","content":"2 1 3"},{"iden":"sample output 1","content":"YES\n1 0 2 3\n\nThe binary representation of $P=(1,0,2,3)$ is $(01,00,10,11)$, where any two adjacent elements differ by exactly one bit."},{"iden":"sample input 2","content":"3 2 1"},{"iden":"sample output 2","content":"NO"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}