Problem3083--TL

3083: TL

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Valera wanted to prepare a Codesecrof round. He's already got one problem and he wants to set a time limit (TL) on it.

Valera has written n correct solutions. For each correct solution, he knows its running time (in seconds). Valera has also wrote m wrong solutions and for each wrong solution he knows its running time (in seconds).

Let's suppose that Valera will set v seconds TL in the problem. Then we can say that a solution passes the system testing if its running time is at most v seconds. We can also say that a solution passes the system testing with some "extra" time if for its running time, a seconds, an inequality 2a≤v holds.

As a result, Valera decided to set v seconds TL, that the following conditions are met:

  1. v is a positive integer;
  2. all correct solutions pass the system testing;
  3. at least one correct solution passes the system testing with some "extra" time;
  4. all wrong solutions do not pass the system testing;
  5. value v is minimum among all TLs, for which points 1, 2, 3, 4 hold.

Help Valera and find the most suitable TL or else state that such TL doesn't exist.

Input

The first line contains two integers n, m (1≤n,m≤100). The second line contains n space-separated positive integers a1,a2,...,an (1≤ai≤100) − the running time of each of the n correct solutions in seconds. The third line contains m space-separated positive integers b1,b2,...,bm (1≤bi≤100) − the running time of each of m wrong solutions in seconds.

Output

If there is a valid TL value, print it. Otherwise, print -1.

Examples
Input
3 6
4 5 2
8 9 6 10 7 11
Output
5
Input
3 1
3 4 5
6
Output
-1

Source/Category

 
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