Mog and Lunarity play the Exit game in an endless underground passage. They start at exit . A correct action advances them from exit to exit , while a wrong action immediately sends them back to exit .
At every exit, one of normal phenomena and abnormal phenomena appears uniformly at random. Mog acts correctly on a normal phenomenon, and Lunarity acts correctly on an abnormal phenomenon.
The players alternate after every action. Returning to exit after a wrong action does not reset whose turn comes next. Mog takes the first action.
Find the expected number of actions required to reach exit for the first time.
The input is given in the following format:
For each test case, write the expectation as a reduced fraction and print .
Each case consists of three positive integers , , and on one line.
