A14216. Array and Peaks

A sequence of $n$ integers is called a permutation if it contains all integers from $1$ to $n$ exactly once.

Given two integers $n$ and $k$ , construct a permutation $a$ of numbers from $1$ to $n$ which has exactly $k$ peaks. An index $i$ of an array $a$ of size $n$ is said to be a peak if $1 < i < n$ and $a_i \gt a_{i-1}$ and $a_i \gt a_{i+1}$ . If such permutation is not possible, then print $-1$ .

The first line contains an integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases.

Then $t$ lines follow, each containing two space-separated integers $n$ ( $1 \leq n \leq 100$ ) and $k$ ( $0 \leq k \leq n$ ) — the length of an array and the required number of peaks.

Output $t$ lines. For each test case, if there is no permutation with given length and number of peaks, then print $-1$ . Otherwise print a line containing $n$ space-separated integers which forms a permutation of numbers from $1$ to $n$ and contains exactly $k$ peaks.

If there are multiple answers, print any.

In the second test case of the example, we have array $a = [2,4,1,5,3]$ . Here, indices $i=2$ and $i=4$ are the peaks of the array. This is because $(a_{2} \gt a_{1} $ , $a_{2} \gt a_{3})$ and $(a_{4} \gt a_{3}$ , $a_{4} \gt a_{5})$ .