'''
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.

 

Example 1:

Input: n = 3, k = 1
Output: "0"
Explanation: S3 is "0111001".
The 1st bit is "0".
Example 2:

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

Constraints:

1 <= n <= 20
1 <= k <= 2n - 1
'''

from typing import *

import unittest


from collections import deque
class Solution:
    def findKthBit(self, n: int, k: int) -> str:
        if n == 1:
            return "0"
        if k < 2 ** (n - 1):
            return self.findKthBit(n - 1, k)
        elif k > 2 ** (n - 1):
            return "1" if self.findKthBit(n - 1, 2 ** n - k) == '0' else '0'
        return "1"

        
class TestSolution(unittest.TestCase):
    def test_case(self):
        examples = (
            ((4, 11), "1"),
        )
        for first, second in examples:
            self.assert_function(first, second)

    def assert_function(self, first, second):
        self.assertEqual(Solution().findKthBit(*first), second,
                         msg="first: {}; second: {}".format(first, second))


unittest.main()

