Find the Permutations

Sorting is one of the most used operations in real life, where Computer Science comes into act. It is well-known that the lower bound of swap based sorting is nlog(n). It means that the best possible sorting algorithm will take at least O(nlog(n)) swaps to sort a set of n integers. However, to sort a particular array of n integers, you can always find a swapping sequence of at most (n − 1) swaps, once you know the position of each element in the sorted sequence. For example consider four elements <1 2 3 4>. There are 24 possible permutations and for all elements you know the position in sorted sequence. If the permutation is <2 1 4 3>, it will take minimum 2 swaps to make it sorted. If the sequence is <2 3 4 1>, at least 3 swaps are required. The sequence <4 2 3 1> requires only 1 and the sequence <1 2 3 4> requires none. In this way, we can find the permutations of N distinct integers which will take at least K swaps to be sorted. Input Each input consists of two positive integers N (1 ≤ N ≤ 21) and K (0 ≤ K < N) in a single line. Input is terminated by two zeros. There can be at most 250 test cases. Output For each of the input, print in a line the number of permutations which will take at least K swaps. Sample Input 31 30 32 00 Sample Output 3 1 2