Fire Inspector
In a chemistry lab, there are N chemical reagents stored on a shelf in special containers. These containers are categorized as either dangerous or safe, based on the fire inspector's professional assessment. According to fire safety regulations, no two dangerous reagents should be placed adjacent to each other. For each instance where this rule is violated, the fire inspector issues a fine of M monetary units, but only to one official within the institution.
What is the maximum total amount the fire inspector can contribute to the state budget, given that he can inspect any number of educational institutions? In each institution, the same number N of chemical reagents is stored, and the arrangement or selection of reagents differs from one institution to another.
Input Data
The input consists of a single line containing two numbers separated by a space: a natural number N (n <= 100000), representing the number of reagents, and a real number M with two decimal places (0 < M < 100000), representing the maximum fine that the fire inspector can impose on one person.
Output Data
Output the maximum amount the fire inspector can contribute to the state budget, formatted to two decimal places.