{"raw_statement":[{"iden":"problem statement","content":"In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between $1$ and $N$ (inclusive) consisting of integers between $1$ and $K$ (inclusive) are listed.\nLet the total number of sequences listed in FEIS be $X$. Among those sequences, find the $(X/2)$\\-th (rounded up to the nearest integer) lexicographically smallest one."},{"iden":"constraints","content":"*   $1 \\leq N,K \\leq 3 × 10^5$\n*   $N$ and $K$ are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$K$ $N$"},{"iden":"sample input 1","content":"3 2"},{"iden":"sample output 1","content":"2 1 \n\nThere are $12$ sequences listed in FEIS: $(1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3)$. The $(12/2 = 6)$\\-th lexicographically smallest one among them is $(2,1)$."},{"iden":"sample input 2","content":"2 4"},{"iden":"sample output 2","content":"1 2 2 2"},{"iden":"sample input 3","content":"5 14"},{"iden":"sample output 3","content":"3 3 3 3 3 3 3 3 3 3 3 3 2 2"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}