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No.2567 A_1 > A_2 > ... > A_N

レベル : / AI推定難易度 : 750 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （解説公開後に AC するまで非表示） / 解いたユーザー数 141
作問者 : Kyo_s_s / テスター : deuteridayo 👑 AngrySadEight kusirakusira Magentor 👑 loop0919 マベマス（mavemas_413） aki
お気に入りにしたユーザー ProblemId : 10346 / 自分の提出
問題文最終更新日: 2023-12-01 20:18:09
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Problem Statement

You are given positive integers $N, X$. Determine whether there exists a sequence $A_1, A_2, \ldots, A_N$ of $N$ positive integers that satisfies all of the following conditions:

  • $A_1 > A_2 > \cdots > A_{N-1} > A_N > 0$
  • $\displaystyle \sum_{i=1}^N A_i = X$

If such a sequence exists, output the lexicographically smallest one.

You are given $T$ test cases; solve each of them.

What is the lexicographic order of sequences of equal length? For $2$ integer sequences of equal length $A=(A_1,A_2,\ldots ,A_N)$ and $B=(B_1,B_2,\ldots ,B_N)$, $A < B$ in lexicographic order is defined to hold if and only if the following is satisfied.
  • There exists an integer $i \ (1 \le i \le N)$ such that $A_j = B_j$ holds for all integers $j$ with $1 \le j < i$, and $A_i < B_i$ holds.

Constraints

  • $1 \leq T \leq 10^5$
  • $1 \leq N \leq 2 \times 10^5$
  • $1 \leq X \leq 10^{18}$
  • Over the test cases contained in $1$ input, the sum of $N$ is at most $2 \times 10^5$
  • All input values are integers

Input

The input is given from standard input in the following format. 

$T$
$\text{case}_1$
$\vdots$
$\text{case}_T$

Each test case $\text{case}_i~(1 \leq i \leq T)$ is given in the following format. 

$N ~ X$

Output

Output $T$ lines. On line $i$, if a sequence satisfying the conditions exists for test case $\text{case}_i$, output that sequence on $1$ line, separated by spaces; otherwise, output $-1$.

Sample

Sample 1
Input
3
4 10
3 5
3 9
Output
4 3 2 1
-1
4 3 2
  • For test case $1$, the only sequence satisfying the $2$ conditions in the problem statement is $(4,3,2,1)$. Thus, output this sequence.
  • For test case $2$, no sequence satisfies the $2$ conditions in the problem statement. Thus, output $−1$.
  • For test case $3$, the sequences satisfying the $2$ conditions in the problem statement are
    • $(6, 2, 1)$
    • $(5, 3, 1)$
    • $(4, 3, 2)$
    and these $3$ are the only ones. Thus, output the lexicographically smallest among them, $(4, 3, 2)$.

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