CF1513A 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}) $ .