There is an empty cup, and a dumb robot is going to fill it with liter of water.

For every turn, the robot will randomly select a real number between and ( is a given number) and then fill the cup with liter of water. The robot will repeat it until the cup is full (at least liter of water has been filled).

You need to answer the expected number of turns the robot should fill.

输入描述:

The first line contains an integer  (), denoting the number of test cases.

In the following  lines, each line contains a real number  (), describing a test case.

It is guaranteed that  contains no more than  decimal places.

输出描述:

For each test case, output one line with a real number, denoting the expected number of turns.

Any answer with a relative or absolute error less than  will be accepted.

2
0.3
1.5

7.3332227396
1.9477340411