1667. Find Kth Bit in Nth Binary String

Medium

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

S₁ = "0"
S_i = S_{i - 1} + "1" + reverse(invert(S_{i - 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 k^th bit in S_n. It is guaranteed that k is valid for the given n.

Example 1:

Input: n = 3, k = 1
Output: "0"
Explanation: S₃ is "0111001".
The 1^st bit is "0".

Example 2:

Input: n = 4, k = 11
Output: "1"
Explanation: S₄ is "011100110110001".
The 11^th bit is "1".

Constraints:

1 <= n <= 20
1 <= k <= 2ⁿ - 1