Primal Collection

You are given an array $A$, which initially has a size of $N$ (indexed from $1$ to $N$) containing distinct integers with values between $1$ and $N + 1$ inclusive. It is known that this array is primal, that is, for any index $i > 1$, $A_i$ is always smaller than $A_{\lfloor i/2 \rfloor}$.

Denote $S$ as the value between $1$ and $N + 1$ that does not appear in $A_1, A_2, \dots, A_N$. You want to append one new element to $A$, namely $A_{N+1}$, with the value $S$. Then the following algorithm is executed.

algorithm(A):
  x = N + 1
  counter = 0
  while x > 1:
    if A[x] > A[floor(x / 2)]:
      swap(A[x], A[floor(x / 2)]);
      counter = counter + 1
    x = floor(x / 2)
  return counter

Count the number of possible initial arrays $A$ such that, after appending $S$ and executing algorithm(A), the algorithm returns $K$. The initial array $A$ contains distinct integers with values between $1$ and $N + 1$ inclusive, excluding $S$, and must be primal. Since the answer can be very large, print it modulo $998\,244\,353$.

A single line with three integers $N$, $S$, $K$ ($1 \le N \le 100\,000$; $1 \le S \le N + 1$; $0 \le K \le N$).

A single integer, the number of possible initial arrays $A$ that satisfy the conditions above, modulo $998\,244\,353$.