USACOTrainning.Ordered Fractions

这题简单，但看到analysis里面的这个解法真是囧。

 

We notice that we can start with 0/1 and 1/1 as our ``endpoints'' and recursively generate the middle points by adding numerators and denominators.

0/1                                                              1/1

                               1/2

                  1/3                      2/3

        1/4              2/5         3/5                 3/4

    1/5      2/7     3/8    3/7   4/7   5/8       5/7         4/5

Each fraction is created from the one up to its right and the one up to its left. This idea lends itself easily to a recursion that we cut off when we go too deep.