Family Reunion

Interview

Time limit1sMemory limit1024 MB

Summary

Given a family tree as a parent array, find the closest common ancestor of M seated people, which may be one of them.

Level: Easy3 of 10
Topics: Tree, Implementation
Solved: No attempts yet

Problem

A family reunion is held for the descendants of Ida-Ottilia Isaksson. For simplicity, a family tree has been drawn up. All descendants are numbered from $1$ to $N$ , and Ida-Ottilia herself is given the number $0$ .

Among the $M$ people at your table, a discussion starts about who their nearest common relative is (closest going up the tree). Write a program that computes this. Note that this sometimes can be someone sitting at the table.

Input

The first line contains the numbers $N$ and $M$ ( $2 \le M \le N \le 20$ ). The second line contains $N$ numbers, the parent of each descendant (all between $0$ and $N$ ). The third line contains $M$ numbers, the people around the table (all between $1$ and $N$ , with no duplicates).

Output

Print a single number: the number of the nearest common relative of the people at the table.

Examples2

Example 1
Input
```
8 3
6 0 0 2 0 5 6 5
1 5 8
```
Expected output
```
5
```
Example 2
Input
```
4 2
2 0 0 3
4 1
```
Expected output
```
0
```