Types: n: int, k: int, a: List[int]
Ranges: 2 ≤ n ≤ 8000, n is even, 0 ≤ k ≤ min(n/2, 20), 1 ≤ a[i] ≤ n, a[i] ≠ i
Addtl Info: a_i ≠ a_j (i ≠ j), a[a_i] = i