Problem D. Dreaming on a train

Author:M. Sporyshev   Time limit:1 sec
Input file:input.txt   Memory limit:256 Mb
Output file:output.txt  


Young programmer Vasya goes to work and from work on the train every day.

When returning from work, Vasya is very tired, so he can fall asleep in the train.

On the route from work to Vasya's home there are N stations. Each of them is announced on the radio at the moment when the train is at the previous station. Vasya's station is announced on the N-th station.

If Vasya hears the name of his station, then he will not miss it for sure.

However, every time Vasya listens to the names of the stations, he can fall asleep with a probability of 0.5. In this case, he won't hear the announcement on the next M stations. After sleeping through the announcement of the station, Vasya would never get off the train on it.

Now Vasya thinks whether to give up such a habit of sleeping on the train. For this, he wants to calculate the probability of oversleeping the announcement of his station.

Input file format

The first line of the input file contains integers N, M — total the number of stations and the number of stations that Vasya will sleep.

Output file format

Output a single number — the probability to oversleep the announcement of the station with an accuracy of at least 5 digits after the decimal point.


1 ≤ M ≤ N ≤ 1000

Sample tests

No. Input file (input.txt) Output file (output.txt)
2 1
3 1

0.038s 0.009s 15