405216: GYM101845 M Marbles Lucky Distribution

Juan have N red marbles, M blue marbles, and K bottles. He will put a certain number of marbles on each of the K bottles such that no bottle remains empty and every marble is inside a bottle.

Andres is a Santa Fe fan, so he will pick one bottle at random with an uniform distribution, then he will pick a marble inside of it at random with an uniform distribution, with the hope is a red marble. As Juan is a Millonarios fan, he wants to distribute the marbles in the bottles such that the probability of Andres picking a blue marble is maximized. Juan has a busy life, therefore he needs your help to determine the best arrangement for the marbles and the probability of Andres getting a blue marble.

The input consist of three integers separated by spaces, N M and K (1 ≤ N, M, K ≤ 10⁹) - the number of red marbles, blue marbles and bottles respectively.

Print the probability of Bob getting a blue marble such that the marble arrangement is optimal. Your answer will be considered correct, if its absolute or relative error does not exceed 10^- 6.

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