Bloodsucker

Time Limit: 2 Seconds
Memory Limit: 65536 KB

In 0th day, there are `n-1` people and 1 bloodsucker.
Every day, two and only two of them meet. Nothing will happen if they are of the same species, that is, a people meets a people or a bloodsucker meets a bloodsucker. Otherwise, people may be transformed into bloodsucker with probability `p`.
Sooner or later(`D` days), all people will be turned into bloodsucker.
Calculate the mathematical expectation of `D`.

#### Input

The number of test cases (`T`, `T` ≤ 100) is given in the first line of the input.
Each case consists of an integer `n` and a float number `p` (1 ≤ `n` < 100000, 0 < `p` ≤ 1, accurate to 3 digits after decimal point), separated by spaces.

#### Output

For each case, you should output the expectation(3 digits after the decimal point) in a single line.

#### Sample Input

1
2 1

#### Sample Output

1.000

Author:

**WU, Yingxin**
Submit
Status