{"raw_statement":[{"iden":"problem statement","content":"You are given integers $N$ and $K$. Determine whether there exists a permutation $P=(P_0,P_1,\\cdots,P_{2^N-1})$ of $(0,1,\\cdots,2^N-1)$ satisfying the condition below, and construct one such sequence if it exists. Note that $P$ is $0$\\-indexed.\n\n*   For every $i$ ($0 \\leq i \\leq 2^N-1$), $P_i$ and $P_{i+1 \\mod 2^N}$ differ by exactly $K$ bits in binary representation. The comparison is made after zero-padding both integers to $N$ bits."},{"iden":"constraints","content":"*   $1 \\leq K \\leq N \\leq 18$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$"},{"iden":"sample input 1","content":"3 1"},{"iden":"sample output 1","content":"Yes\n0 1 3 2 6 7 5 4\n\nHere, we have $P=(000,001,011,010,110,111,101,100)$ in binary representation.\nWe can see that $P_1=001$ and $P_2=011$, for example, differ by exactly $1$ bit, satisfying the condition for $i=1$. The same goes for every $i$."},{"iden":"sample input 2","content":"2 2"},{"iden":"sample output 2","content":"No"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}