{"problem":{"name":"Non-triangular Triplets","description":{"content":"Given are positive integers $N$ and $K$. Determine if the $3N$ integers $K, K+1, ..., K+3N-1$ can be partitioned into $N$ triples $(a_1,b_1,c_1), ..., (a_N,b_N,c_N)$ so that the condition below is sat","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"nikkei2019_2_qual_e"},"statements":[{"statement_type":"Markdown","content":"Given are positive integers $N$ and $K$.\nDetermine if the $3N$ integers $K, K+1, ..., K+3N-1$ can be partitioned into $N$ triples $(a_1,b_1,c_1), ..., (a_N,b_N,c_N)$ so that the condition below is satisfied. Any of the integers $K, K+1, ..., K+3N-1$ must appear in exactly one of those triples.\n\n*   For every integer $i$ from $1$ to $N$, $a_i + b_i \\leq c_i$ holds.\n\nIf the answer is yes, construct one such partition.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq K \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"nikkei2019_2_qual_e","tags":[],"sample_group":[["1 1","1 2 3"],["3 3","\\-1"]],"created_at":"2026-03-03 11:01:13"}}