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!

### Input

In the only line there are three integers: *N* (1 ≤ *N* ≤ 10^{9}), *M* (0 ≤ *M* ≤ *N*), *K* (0 ≤ *K* ≤ 1000).

### Output

Output the answer as an irreducible fraction *p*/*q*.

### Samples

input | output |
---|

1 1 9 | 0/1 |

5 4 3 | 353/125 |

**Problem Source: **SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008.