ZOJ Problem Set - 3380
Patchouli Knowledge, the unmoving great library, is a magician who has settled down in the Scarlet Devil Mansion (紅魔館). Her specialty is elemental magic employing the seven elements fire, water, wood, metal, earth, sun, and moon. So she can cast different spell cards like Water Sign "Princess Undine", Moon Sign "Silent Selene" and Sun Sign "Royal Flare". In addition, she can combine the elements as well. So she can also cast high-level spell cards like Metal & Water Sign "Mercury Poison" and Fire, Water, Wood, Metal & Earth Sign "Philosopher's Stones" .
Assume that there are m different elements in total, each element has n different phase. Patchouli can use many different elements in a single spell card, as long as these elements have the same phases. The level of a spell card is determined by the number of different elements used in it. When Patchouli is going to have a fight, she will choose m different elements, each of which will have a random phase with the same probability. What's the probability that she can cast a spell card of which the level is no less than l, namely a spell card using at least l different elements.
There are multiple cases. Each case contains three integers 1 ≤ m, n, l ≤ 100. Process to the end of file.
For each case, output the probability as irreducible fraction. If it is impossible, output "mukyu~" instead.
7 6 5 7 7 7 7 8 9
187/15552 1/117649 mukyu~
Author: WU, Zejun
Source: ACM × Touhou
Contest: ZOJ Monthly, August 2010