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.