{"problem":{"name":"Finite Encyclopedia of Integer Sequences","description":{"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. Let the total nu","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc084_c"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $1 \\leq N,K \\leq 3 × 10^5$\n*   $N$ and $K$ are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$K$ $N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc084_c","tags":[],"sample_group":[["3 2","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 $(2,1)$."],["2 4","1 2 2 2"],["5 14","3 3 3 3 3 3 3 3 3 3 3 3 2 2"]],"created_at":"2026-03-03 11:01:14"}}