Inverse Descent Permutations

A permutation A = (A_0, A_1, ..., A_{N-1}) of length N contains each integer from 0 to N-1 exactly once. Let B = (B_0, B_1, ..., B_{N-1}) be the inverse permutation of A, so B_{A_i} = i. For example, if A = (2, 0, 3, 1, 4), then B = (1, 3, 0, 2, 4).

If the inverse permutation B has exactly K indices i such that B_i > B_{i+1}, call A a permutation with K inverse descents.

Given N, K, and F, count the permutations A such that A_0 = F and A has exactly K inverse descents.

The first line contains N, the second line contains K, and the third line contains F.

Print the number of permutations satisfying the condition.

• 1 <= N <= 20
• 0 <= K <= N-1
• 0 <= F <= N-1