1834. Factorial Digits

In the factorial number system, the digit at position i, counting 1 from the right, is multiplied by i! and may be anything from 0 to i. Every non-negative integer can be written this way in exactly one way with no leading zeros, so n equals d_k * k! + d_(k-1) * (k-1)! + ... + d_1 * 1!, where each d_i is between 0 and i and the leading digit d_k is not 0.

Given the integer n, return the digits d_k, d_(k-1), ..., d_1 as an array, most significant first. For n = 0 return [0]. For example, 463 is [3, 4, 1, 0, 1] because 3*120 + 4*24 + 1*6 + 0*2 + 1*1 = 463. Aim for O(k) time, where k is the number of digits in the answer.