Keys In Boxes#1531
There are boxes numbered from to , and keys, also numbered from to . The -th key can open only the -th box. Each key is randomly placed into one of the boxes in such a way that each box contains exactly one key. All possible placements of the keys are equally likely. After that, all boxes are locked.
You have bombs, each of which can open one locked box. After opening a box using a bomb, you can take the key inside and, if necessary, use it to open another locked box (provided that this key does not belong to the box that was just opened). Continue this process: open boxes using bombs, take the keys, and use them to open other boxes whenever possible.
Compute the probability that you will be able to open all the boxes in this way.
Each line contains two integers n(1 \le n \le 20) and m~(1 \le m \le n).
For each test case, print the probability of opening all boxes in the form "A/B", where and are positive coprime integers without leading zeros.
Example 1