Problem Statement

Ooka, who lives in the Great Okayama Empire, can use magic.

Being able to use magic, Ooka heard a rumor about a mysterious pocket that, when tapped while containing $M$ biscuits, makes the number of biscuits inside $M + 1$, and he decided to try making something similar himself.

However, he thought that he wouldn't be all that happy no matter how many biscuits he got, and that increasing them only one at a time was inefficient... So, after much trial and error, he succeeded in making the following knapsack that increases money.

When the knapsack contains $M$ yen and is tapped once,

• with probability 1/3, its content becomes $M \times 2$ yen
• with probability 1/3, its content becomes $M + 1$ yen
• with probability 1/3, its content becomes $0$ yen

(The result of each trial is independent, regardless of the results before and after it, the state of the content, and so on.)

However, Ooka became very worried about whether he could actually increase his money using this knapsack.

So, for Ooka's sake, find the expected value of the amount of money in the knapsack after tapping a knapsack that initially contains $M$ yen exactly $N$ times.

Input

$M$ $N$

The amount $M$ initially in the knapsack and the number of times $N$ the knapsack is tapped are given on one line, separated by a space.

All inputs are integers and satisfy the following constraints.

• $0 \leq M, N \leq 1000$

Output

Output the amount of money in the knapsack after tapping it exactly $N$ times.

An error of at most $10^{-8}$ is allowed.

Sample

100 2

100.666666666667

0 30

10

114 514

285.333333333333