Fleytitala

Image from flickr.com

Friðrik is killing time by skipping stones. He’s getting so good at it that he can decide how often the stone will bounce.

Friðrik starts by throwing the stone $d$ meters. After each bounce the distance the stone travels is cut in half. How many meters does the stone travel in total?

The input consists of two lines. The first line contains one integer $0 \leq d \leq 10^6$, the distance that the stone will travel before bouncing. The second line contains one integer $0 \leq k \leq 10^{18}$, the number of bounces.

Print a single line with a floating point number, the total distance that the stone travels.

The output is considered correct if the number has a relative or absolute error of at most $10^{-5}$ from the correct answer. This means it doesn’t matter how many significant digits the answer contains as long as it’s accurate enough.

Group |
Points |
Constraints |

1 |
25 |
$0 \leq k \leq 10$ |

2 |
50 |
$0 \leq k \leq 1\, 000$ |

3 |
25 |
No further constraints |

Sample Input 1 | Sample Output 1 |
---|---|

1 1 |
1.5 |

Sample Input 2 | Sample Output 2 |
---|---|

12 4 |
23.25 |

Sample Input 3 | Sample Output 3 |
---|---|

0 10 |
0.0 |