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 Pi+Pi+1≥K for each 1≤i<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≤i≤N such that P1=Q1,P2=Q2,… and Pi<Qi.
Input format
Output format
For each test case, print −1 if no suitable permutation exists, otherwise print the lexicographically smallest permutation satisfying the conditions.
Constraints
1≤T≤1052≤N≤3⋅1051≤K≤2⋅NSum of N over all test cases does not exceed 3⋅105.