Lottery

Jimin chooses M distinct numbers from 1 through N. The lottery also chooses M distinct numbers from 1 through N.

Jimin wins if at least K numbers appear in both choices. Compute the probability that Jimin wins.

The first line contains three integers N, M, and K, separated by spaces.

Print the probability that Jimin wins. An absolute or relative error of at most 10^{-9} is accepted.

• 2 <= N <= 8
• 1 <= M <= N-1
• 1 <= K <= M