779. K-th Symbol in Grammar

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Problem

We build a table of n rows (1-indexed). We start by writing 0 in the $1^{st}$ row. Now in every subsequent row, we look at the previous row and replace each occurrence of 0 with 01, and each occurrence of 1 with 10.

• For example, for n = 3, the $1^{st}$ row is 0, the $2^{nd}$ row is 01, and the $3^{rd}$ row is 0110.

Given two integer n and k, return the $k^{th}$ (1-indexed) symbol in the $n^{th}$ row of a table of n rows.

Example 1:

Input: n = 1, k = 1
Output: 0
Explanation: row 1: 0

Example 2:

Input: n = 2, k = 1
Output: 0
Explanation:
row 1: 0
row 2: 01

Example 3:

Input: n = 2, k = 2
Output: 1
Explanation:
row 1: 0
row 2: 01

Constraints:

• 1 <= n <= 30
• $1<=k<=2^{n-1}$

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