Execution time limit is 1 second

Runtime memory usage limit is 64 megabytes

There are n boxes numbered from 1 to n and n keys numbered from 1 to n. The i-th key can only be used to open the i-th box. Now, we randomly put exactly one key into each of the boxes. We assume that all configurations of keys in boxes occur with the same probability. Then we lock all the boxes. You have m bombs, each of which can be used to open one locked box. Once you open a locked box, you can get the key in it and perhaps open another locked box with that key. Your strategy is to select a box, open it with a bomb, take the key and open all the boxes you can and then repeat with another bomb.

Find the probability that you can get all the keys.

Each line contains two integers n (1 ≤ n ≤ 20) and m (1 ≤ m ≤ n).

For each test case in a separate line print the probability that you can get all the keys. The output value must be formatted as "A/B" (quotes for clarity), representing the probability as a fraction. A and B must both be positive integers with no leading zeroes, and the greatest common divisor of A and B must be 1.

Input #1

Answer #1