{"problem":{"name":"「WHOI-2」ぽかぽかの星","description":{"content":"有多少个长度为 $n$ 的**正整数**数列 $a_i$ 满足： - $0<a_1\\leq a_2\\leq a_3\\dots \\leq a_n\\leq k$。 - $\\forall i\\not = j,a_i+a_j\\not = k+1$。 答案对 $10^9+7$ 取模。","description_type":"Markdown"},"platform":"Luogu","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":{"LuoguStyle":"P4"},"is_remote":true,"is_sync":true,"sync_url":null,"sign":"LGP8432"},"statements":[{"statement_type":"Markdown","content":"有多少个长度为 $n$ 的**正整数**数列 $a_i$ 满足：\n\n- $0<a_1\\leq a_2\\leq a_3\\dots \\leq a_n\\leq k$。\n- $\\forall i\\not = j,a_i+a_j\\not = k+1$。\n\n答案对 $10^9+7$ 取模。\n\n## Input\n\n**本题多测**\n\n第一行一个正整数表示 $T$。\n\n接下来 $T$ 行，每行两个正整数表示 $n,k$。\n\n## Output\n\n$T$ 行，每行一个正整数表示答案。\n\n[samples]\n\n## Background\n\n![](bilibili:BV16J411x7nS)\n\n你在雪洞里喝着热可可数星星。但这次，星星换成了数列，不过聪明的你一定能数清楚数列的吧。\n\n## Note\n\n**本题采用捆绑测试**\n\n- $\\text{subtask1(20pts)}:T=5,1\\leq n,k\\le5$。\n- $\\text{subtask2(80pts)}:$ 无特殊限制。\n\n对于 $100\\%$ 的数据，$T\\leq100,1\\le n,k\\le 5\\times 10^6,1\\leq  \\sum n,  \\sum  k\\le6\\times 10^7$。","is_translate":false,"language":"English"}],"meta":{"iden":"LGP8432","tags":["数学","洛谷原创","O2优化"],"sample_group":[["3\n2 2\n1145 1419\n19198 12321","2\n66937457\n949924930"]],"created_at":"2026-03-03 11:09:25"}}