Inside a rope of length n, n-1 points are placed with distance 1 from each other and from the endpoints. Among these points, we choose m-1 points at random and cut the rope at these points to create m segments.
Let E(n, m) be the expected length of the shortest segment. Give n and m, find E(n, m).
Give your answer rounded to 5 decimal places behind the decimal point.
The first line of input will be a positive integer T indicating how many data sets will be included. Each of the next T lines will contain two integers n, m (1 ≤ n, m ≤ 100000; m ≤ n) as mentioned before.
For each test case, output E(n, m) rounded to 5 decimal places behind the decimal point in separate line.