Chirag wanted to prepare a Programmin round. He's already got one problem and he wants to set a time limit (TL) on it.
Chirag has written n correct solutions. For each correct solution, he knows its running time (in seconds). Chirag has also wrote m wrong solutions and for each wrong solution he knows its running time (in seconds).
Let's suppose that Chirag 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, Chirag 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 Chirag 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.