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 $[]$.