Find Kth Bit in Nth Binary String

Description

Given two positive integers n and k, the binary string Sn is formed as follows:

- S1 = "0"

- Si = Si - 1 + "1" + reverse(invert(Si - 1)) for i > 1

Where + denotes the concatenation operation, reverse(x) returns the reversed string x, and invert(x) inverts all the bits in x (0 changes to 1 and 1 changes to 0).

For example, the first four strings in the above sequence are:

- S1 = "0"

- S2 = "011"

- S3 = "0111001"

- S4 = "011100110110001"

Return the kth bit in Sn. It is guaranteed that k is valid for the given n.