C. United We Stand Divided We Fall
time limit per test
6 s
memory limit per test
256 MB
input
standard input
output
standard output
                  "Teamwork is everything                           Take the ball                           Pass the ball"
— Pep Algorithmola

The great football coach Pep Algorithmola hired Da7doo7(after he got fired again) to solve this problem for him because unlike football he is bad at math and so is Da7doo7 so he asked you to solve it.

He has a team of $$$n$$$ members numbered from $$$1$$$ to $$$n$$$. They are standing in a circle in the order of their numbers and pass the ball each to the next player the game starts from the smallest index ($$$1$$$ to $$$2$$$, $$$2$$$ to $$$3$$$, $$$\ldots$$$, $$$n-1$$$ to $$$n$$$, $$$n$$$ to $$$1$$$) and when a player gets tired from receiving balls he passes the ball one last time and leaves the circle. When only one person remains in the circle, he is announced as the winner and thus leaves the circle.

You know that each team member has strength $$$S_i$$$ which denotes that the $$$i$$$-th person passes the ball with strength $$$S_i$$$, and health $$$H_i$$$ which means that this person leaves the circle when the sum of strengths of all the passes he received is greater than or equal to $$$H_i$$$.

The coach wants to know the order in which his players will leave the circle. Can you help him find it?

Input

The first line contains a single integer $$$T$$$ ($$$1 \le T \le 10^5$$$) denoting the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 10^6$$$) denoting the number of players.

The second line of each test case contains $$$n$$$ positive integers $$$H_1, H_2, \ldots, H_n$$$ ($$$1 \le H_i \le 10^9$$$) indicating the health of each player.

The third line of each test case contains $$$n$$$ positive integers $$$S_1, S_2, \ldots, S_n$$$ ($$$1 \le S_i \le 10^9$$$) indicating the strength of each player.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$.

Output

For each test case, output in a separate line the order in which the players will leave the circle.

Example
Input
2
5
4 5 6 2 1
2 2 2 1 4
2
1 1
1 1
Output
4 5 1 2 3 
2 1