March 28 ADA University Students + Schoolchildren

Expected Minimum Power

Time limit 1 second
Memory limit 128 MiB

You are given two positive integers n and x.

You are going to choose x distinct integers, each between 1 and n, inclusive. The choice will be made uniformly at random. That is, each of the possible x-element subsets of the integers 1 to n is equally likely to be chosen.

Let S be the smallest integer among the x chosen ones. Compute the expected value of 2^S. In other words, determine the average value of 2 to the power of S, where the average is taken over all possible choices of the x distinct integers.

Input data

Two positive integers: n (1n50) and x (1xn).

Output data

Print the average value of 2 to the power of S with 4 decimal digits.


Input example #1
4 4
Output example #1
Input example #2
3 2
Output example #2


In the first test case the only possible situation is that you will choose (1, 2, 3, 4). In this case, the minimum is 1, and the expected value is 2^1 = 2.

In the second test case there are three equally likely scenarios: you will select either {1, 2} or {1, 3} or {2, 3}. The corresponding values of S are 1, 1 and 2 respectively. Thus, the average value of 2^S is (2^1 + 2^1 + 2^2) / 3 = 8 / 3 = 2.6666666.