Maximum in the Cycle of 1#3558
If is a permutation of the integers , ..., , the maximum in the cycle of is the maximum of the values , , P(P(P(1))), etc. For example, if is the permutation:
|1\ 2\ 3\ 4\ 5\ 6\ 7\ 8| |3\ 2\ 5\ 4\ 1\ 7\ 8\ 6|
we have:
P(1) = 3, P(P(1)) = P(3) = 5
and
P(P(P(1))) = P(5) = 1
so the maximum in the cycle of is .
For this problem, you will write a program which takes as input integers (n > 0) and (1 \le k \le n), and returns the number of permutations of the integers , ..., , for which the maximum in the cycle of is .
The first line of input contains a single integer (1 \le P \le 1000), which is the number of data sets that follow. Each data set is a single line that contains the three space separated decimal integer values. The first value is the data set number . The second value is the size of the permutation, (1 \le n \le 20), and the third value is the desired maximum in the cycle of , (1 \le k \le n).
For each data set there is one line of output. It contains the data set number followed by a single space, followed by a double precision floating point whole value which is the number of permutations of the integers , ..., , for which the maximum in the cycle of is .
Example 1