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## 1620. Clever House

Ограничение времени: 2.0 секунды
Ограничение памяти: 64 МБ
Little boy Vasya likes high-end technologies. Recently he read about "clever houses", where everything is managed automatically, and decided to make his house "clever". To begin with, he connected all N light-bulbs to his computer, which will help to manage the lighting level and save the energy.
Little hacker Petr, who lives nearby, decided to make a nasty thing to Vasya. He created a computer virus. The main action of this virus is to select a random light-bulb and change its state (to switch off if it was on, and vice versa). This action is repeated for K times.
At the beginning there were M light bulbs turned on. Now Petr wants to know how efficient his attack will be. More precisely, he wants to know how much light-bulbs in average will be on after the virus is activated (the mathematical expectation of this value). Help him in this complex task!

### Исходные данные

In the only line there are three integers: N (1 ≤ N ≤ 109), M (0 ≤ MN), K (0 ≤ K ≤ 1000).

### Результат

Output the answer as an irreducible fraction p/q.

### Примеры

исходные данныерезультат
1 1 9
0/1
5 4 3
353/125
Источник задачи: SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008.
Метки: нет