Casino
Kotyhoroshko and Pan Kotsky traveled from Italy to Monte Carlo, while Vernyhora headed to Germany to watch boxing matches. Naturally, in Monte Carlo, both Kotyhoroshko and Pan Kotsky couldn't resist the allure of the casino. They were particularly drawn to a slot machine called "Separated Couple," which was similar to a "one-armed bandit." This machine stood out because it featured N reels (2 ≤ N ≤ 100), with each reel displaying M different images (2 ≤ M ≤ 10,000,000). The total number of possible image combinations on the reels of the "Separated Couple" did not exceed 10^15.
The machine earned its name because a winning combination occurred when exactly two reels, which were not adjacent, displayed the same image, while all other reels showed different images. Pan Kotsky was curious about the probability of such a winning combination appearing on the "Separated Couple" slot machine. Your task is to help him determine this probability. The result should be calculated with D decimal places without rounding (2 ≤ D ≤ 1000).
Input
The input consists of three integers separated by spaces: N M D.
Output
Output a single number representing the probability of a winning combination appearing on the reels of the "Separated Couple."