{"problem":{"name":"Hated Number","description":{"content":"You are given positive integers $X, M \\ (X \\leq M)$. You like positive integers less than or equal to $M$, but you hate $X$ as the exception. So you decide to construct a set $S$ satisfying the follow","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"1202Contest_j"},"statements":[{"statement_type":"Markdown","content":"You are given positive integers $X, M \\ (X \\leq M)$.\nYou like positive integers less than or equal to $M$, but you hate $X$ as the exception. So you decide to construct a set $S$ satisfying the following conditions.\n\n*   $S$ consists of distinct positive integers less than or equal to $10^5$.\n*   $S$ has at most $20$ elements.\n*   For all positive intergers $k$ satisfying $1 \\leq k \\leq M$ and $k \\neq X$, there exists at least one subset of $S$ such that the sum of its elements equals to $k$.\n*   There is no subset of $S$ such that the sum of its elements equals to $X$.\n\nDetermine whether such a set $S$ exists, and if so, construct one example.\nSolve $T$ test cases for each input file.\n\n## Constraints\n\n*   $1 \\leq T \\leq 100$\n*   $1 \\leq X \\le M \\leq 10^5$\n*   $M \\geq 2$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$T$\n$\\mathrm{case}_1$\n$\\vdots$\n$\\mathrm{case}_T$\n\nEach test case is given in the following format:\n\n$X \\ M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"1202Contest_j","tags":[],"sample_group":[["3\n4 6\n3 7\n11 11","3\n1 2 5\n-1\n4\n1 2 3 4\n\n*   In the first case, $S=\\lbrace 1, 2, 5 \\rbrace$ is one example of $S$．\n*   In the second case, there is no $S$ satisfying the conditions.\n*   In the third case, $S=\\lbrace 1, 2, 3, 4 \\rbrace$ is one example of $S$．"]],"created_at":"2026-03-03 11:01:13"}}