SP9642 GETFAST - Getting There Fast

_Original statement in spanish at _ Gabriela drives a school bus. Being one of the few women who have that job, she is always mocked by the male drivers. To improve her status, she decided that besides driving responsibly she is going to drive more efficiently. Her idea is to finish her route spending as little time as possible, without violating any traffic rule. The bus Gabriela drives has a very modern driving system that allows her to adjust the acceleration to any real number instantly. Hence, the acceleration is constant by intervals, jumping to another acceleration whenever Gabriela decides so. If _v_ is the bus' speed at a given instant of time, and _a_ its acceleration that remains constant over a period of time _t_, then the speed at the end of that period will be _v + at_. Moreover, the bus will move a distance of _at $ ^{2} $ /2 + vt_ during that period of time. The traffic rules prevent vehicles from using an acceleration greater than **A**, or a deceleration less than **D**, i.e. the acceleration _a_ at any time must satisfy -**D**

The input contains several test cases. Each test case is described using several lines. The first line of each test case contains four integers **N**, **L**, **A** and **D**. **N** represents the total number of check points that are present in Gabriela's route (1

For each test case, output a single line containing a rational that represents the minimum time (in seconds) needed for Gabriela to finish her route without violating any traffic rule, or an asterisk if it is impossible to do that. Round the answer to the nearest rational with two decimal digits. In case of a tie, round up. Print exactly two digits after the decimal point, even if that means ending the number with 0's.