List Removals

You are given a list consisting of n integers. Your task is to remove elements from the list at given positions, and report the removed elements.

Input

The first input line has an integer n: the initial size of the list. During the process, the elements are numbered 1,2,\dots,k where k is the current size of the list. The second line has n integers x_1,x_2,\dots,x_n: the contents of the list. The last line has n integers p_1,p_2,\dots,p_n: the positions of the elements to be removed.

Output

Print the elements in the order they are removed.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le x_i \le 10^9$

$1 \le p_i \le n-i+1$

Example

Input

5
2 6 1 4 2
3 1 3 1 1

Output

1 2 2 6 4

Explanation: The contents of the list are [2,6,1,4,2], [2,6,4,2], [6,4,2], [6,4], [4] and [].