{"raw_statement":[{"iden":"problem statement","content":"Determine if there exists a sequence obtained by permuting $1,2,...,N$ that satisfies the following conditions:\n\n*   The length of its longest increasing subsequence is $A$.\n*   The length of its longest decreasing subsequence is $B$.\n\nIf it exists, construct one such sequence."},{"iden":"notes","content":"A subsequence of a sequence $P$ is a sequence that can be obtained by extracting some of the elements in $P$ without changing the order.\nA longest increasing subsequence of a sequence $P$ is a sequence with the maximum length among the subsequences of $P$ that are monotonically increasing.\nSimilarly, a longest decreasing subsequence of a sequence $P$ is a sequence with the maximum length among the subsequences of $P$ that are monotonically decreasing."},{"iden":"constraints","content":"*   $1 \\leq N,A,B \\leq 3\\times 10^5$\n*   All input values 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":"5 3 2"},{"iden":"sample output 1","content":"2 4 1 5 3\n\nOne longest increasing subsequence of this sequence is ${2,4,5}$, and one longest decreasing subsequence of it is ${4,3}$."},{"iden":"sample input 2","content":"7 7 1"},{"iden":"sample output 2","content":"1 2 3 4 5 6 7"},{"iden":"sample input 3","content":"300000 300000 300000"},{"iden":"sample output 3","content":"\\-1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}