Given 2 integers n and start. Your task is return any permutation p of (0,1,2…..,2^n -1) such that :

p[0] = start

p[i] and p[i+1] differ by only one bit in their binary representation.

p[0] and p[2^n -1] must also differ by only one bit in their binary representation.

Example 1:
Input: n = 2, start = 3 Output: [3,2,0,1] Explanation: The binary representation of the permutation is (11,10,00,01). All the adjacent element differ by one bit. Another valid permutation is [3,1,0,2]
Example 2:
Input:n = 3, start = 2 Output: [2,6,7,5,4,0,1,3] Explanation: The binary representation of the permutation is (010,110,111,101,100,000,001,011).

Constraints:

1 <= n <= 16

0 <= start < 2 ^ n

Solution

Its a problem of generating a Gray code, Only twist we have here is we need to rotate a result list till we get first number as start number.

Code

Output

[2, 6, 7, 5, 4, 0, 1, 3]

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