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: v is a positive integer; all correct solutions pass the system testing; at least one correct solution passes the system testing with some "extra" time; all wrong solutions do not pass the system testing; 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 a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 100) — the running time of each of the n correct solutions in seconds. The third line contains m space-separated positive integers b_1, b_2, ..., b_{m} (1 ≤ b_{i} ≤ 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