Problems

Bike

The cyclist is going to drive from point A to point B, the distance between them is l m. He has a bike that can reach the speed v m/sec. But before leaving the cyclist can do some upgrading for his bike. For each modernization it is known how much it increases the speed of the bike, as well as the time in which it can be done. He can perform any number of different upgrades, but each upgrade can be performed no more than once. Help the cyclist to reach the point B as soon as possible.

Input

First goes three integers: the distance between the points l (0l109), initial speed of the bike v (1v106) and number of different upgrades n (0n100). Next n pairs of integers are given, each defining the corresponding modernization: the speed increase after modernization vi (0vi1000) and time ti (0ti1000) spent for this upgrade. All values are given in meters and seconds.

Output

Print the minimal time with six digits after the decimal point, in which the cyclist will drive from point A to point B taking into account the modernization time.

Time limit 1 second
Memory limit 122.17 MiB
Input example #1
100 5 1 3 10

Output example #1
20.000000

Input example #2
100 5 2 5 3 5 3

Output example #2
12.666667

Author ΠΠ΅ΡΠΏΠΈΡΠ½ΡΠΉ ΠΠΈΡΠ°Π»ΠΈΠΉ
Source 2010 Tournament of Champions, Vinnica