A new starport has just started working. Starting from some moment of time (call it minute 0), a new spaceship arrives at the starport every M minutes. In other words, spaceships arrive at the starport at minutes 0, M, 2*M, 3*M and so on. 



Similarly, starting from minute 0 and repeating each N minutes, all arrived spaceships that are still placed at the port are teleported to the shed. If a spaceship arrives at the exact same minute when such a teleportation happens, it will be teleported immediately. Otherwise it will need to wait until the next teleportation happens.



Let the waiting time of a spaceship be the time between its arrival and its teleportation to the shed. Return the average waiting time of a spaceship in minutes. See notes for an exact definition.

Each case give you two integer N and M
N and M will each be between 1 and 1,000,000,000, inclusive.

Output the average waiting time of a spaceship in minutes.
Attention, just output one after the decimal point.

4 2
5 3
6 1

1.0
2.0
2.5