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))fori > 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 4 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.
Example 1:
Input: n = 3, k = 1 Output: "0" Explanation: S3 is "0111001". The first bit is "0".
Example 2:
Input: n = 4, k = 11 Output: "1" Explanation: S4 is "011100110110001". The 11th bit is "1".
Example 3:
Input: n = 1, k = 1 Output: "0"
Example 4:
Input: n = 2, k = 3 Output: "1"
Constraints:
1 <= n <= 201 <= k <= 2n - 1