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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 4 strings in the above sequence are:

  • S= "0"
  • S= "011"
  • S= "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 <= 20
  • 1 <= k <= 2n - 1

Solutions

Python3

Java

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