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K-th Symbol in Grammar

We build a table of n rows (1-indexed).

We build a table of n rows (1-indexed). We start by writing 0 in the 1st 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.

Given two integer n and k, return the kth (1-indexed) symbol in the nth 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 <= 2n - 1

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