A permutation of length \(N\) is an array of \(N\) integers such that every integer from \(1\) to \(N\) appears exactly once. For example, \([2, 3, 5, 4, 1] \) is a permutation of length \(5\), while \([1,2, 2], [4, 5, 1, 3] \) are not permutations.

You are given two integers \(N,K\). Find a permutation \(P\) of length \(N\) such that \(P_i + P_{i+1} \ge K\) for each \(1\le i \lt N\). If there are multiple permutations find the lexicographically smallest one. Print \(-1\) if no such permutation exists.

A permutation \(P\) is lexicographically smaller than a permutation \(Q\) of the same length \(N\) if there exists an index \(1\le i \le N\) such that \(P_1 = Q_1, P_2 = Q_2, \dots\) and \(P_i \lt Q_i\).

Input format

• The first line of input contains an integer \(T\) denoting the number of test cases. The description of each test case is as follows:
• The first line of each test case contains two integers \(N,K.\)

Output format

For each test case, print \(-1\) if no suitable permutation exists, otherwise print the lexicographically smallest permutation satisfying the conditions.

Constraints