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There are n students who will be divided into teams where each team consists of k students. Each team is formed by randomly selecting k distinct students from the n students. The problem is to compute the expected number of teams that will be formed when all n students are split into teams of size k.
The input consists of two integers n and k (1 ≤ k ≤ n ≤ 10^6) — the total number of students and the size of each team.
Output a single number — the expected number of teams formed. Your answer should have an absolute or relative error of at most 10^-9.
1 ≤ k ≤ n ≤ 10^6
Example 1
Input
8 2
Output
4.0000000000
Explanation
With 8 students and team size 2, the expected number of teams is exactly 4.