Hated Number

AtCoder

ID1202Contest_j

Time2000ms

Memory256MB

Difficulty—

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 following conditions. * $S$ consists of distinct positive integers less than or equal to $10^5$. * $S$ has at most $20$ elements. * 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 $k$. * There is no subset of $S$ such that the sum of its elements equals to $X$. Determine whether such a set $S$ exists, and if so, construct one example. Solve $T$ test cases for each input file. ## Constraints * $1 \leq T \leq 100$ * $1 \leq X \le M \leq 10^5$ * $M \geq 2$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\vdots$ $\mathrm{case}_T$ Each test case is given in the following format: $X \ M$ [samples]

Samples

Input #1

Output #1

3
1 2 5
-1
4
1 2 3 4

*   In the first case, $S=\lbrace 1, 2, 5 \rbrace$ is one example of $S$．
*   In the second case, there is no $S$ satisfying the conditions.
*   In the third case, $S=\lbrace 1, 2, 3, 4 \rbrace$ is one example of $S$．

API Response (JSON)

{
  "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 follow...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments