Consider a certain permutation of integers from \(1\) to \(n\) as \(​​​​A = \{a_1, a_2,..., a_n\}\) and reverse of array \(A\) as \(R\), that is, \(R = \{a_n, a_{n -1},...,a_1\}\). You are given the inversions at each position of array \(A\) and \(R\) as \(\{IA_1, IA_2,….., IA_n\}\) and \(\{IR_1, IR_2,….., IR_n\}\) respectively.

Find the original array \(A\). If, there are multiple solutions, print any of them. If there is no solution, then print -1.

Note: The inversion of array \(arr\) for position \(i\) is defined as the count of positions \(j\) satisfying the following condition \(arr_j > arr_i\) and \(1 \leq j < i\).

Input format

• The first line contains \(T\) denoting the number of test cases.
• For each test case:
  • The first line contains \(n\) denoting the number of elements.
  • The second line contains the elements \(\{IA_1, IA_2,….., IA_n\}\).
  • The third line contains the elements \(\{IR_1, IR_2,….., IR_n\}\).

Output format

For each test case, print the array \(A\) in the space-separated format or -1 if no solution exists. Each test case should be answered in a new line. 

Constraints 

\(1 \leq T \leq 10 \\ 1 \leq n \leq 10^5 \\ 0 \leq IA_i, IR_i <n \space \forall \space i \in [1, n]\)