A. Array and Peaks
constructive algorithms; implementation
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 \((a_{4} \gt a_{3}\), \(a_{4} \gt a_{5})\).