Leetcode 1545. Find Kth Bit in Nth Binary String

Given S1 = "0" and Si = S{i-1} + "1" + reverse(invert(S{i-1})), return the k-th bit of S_n. Use the string's length (2^n−1) and its central symmetry/inversion property to compute the bit recursively by reflecting k across the middle and flipping bits as needed, avoiding full string construction.