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!

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

Output the answer as an irreducible fraction p/q.