LIS ∩ LDS

AtCoder

IDarc206_d

Time2000ms

Memory256MB

Difficulty—

Among the elements of a permutation $P=(P_1,\ldots,P_N)$ of $(1,\ldots,N)$, those that satisfy the following condition are called good elements: * The element can be included in both a longest increasing subsequence and a longest decreasing subsequence of $P$. You are given integers $N$ and $K$. Determine whether there exists a permutation $P$ of $(1,\ldots,N)$ such that there are exactly $K$ good elements, and if it exists, find one. Answer for $T$ test cases. ## Constraints * All input values are integers * $1 \leq T \leq 2\times 10^5$ * $1 \leq N \leq 2\times 10^5$ * $0\leq K \leq N$ * The sum of $N$ over all test cases does not exceed $2\times 10^5$. ## 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: $N$ $K$ [samples]

Samples

Input #1

Output #1

\-1
7 4 6 2 3 1 5
-1

In the $2$\-nd test case, $P_4=2$ and $P_5=3$ are good elements.
Indeed, $(2,3,5)$ is a longest increasing subsequence of $P$. Also, $(7,6,2,1)$ and $(7, 6, 3, 1)$ are longest decreasing subsequences of $P$.
Therefore, in this sample output, $2$ and $3$ are good elements. The other elements are not good elements, so this output satisfies the condition.
In the $1$\-st and $3$\-rd test cases, there does not exist a permutation satisfying the condition. Thus, output `-1`.

API Response (JSON)

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