Fizzbuzz in any base Challenge

Input:

An integer \$b\$ between 2 and 62 (inclusive).

Output:

Count from \$1\$ to the equivalent of \$5000_{10}\$ in base \$b\$, using any reasonable representation for the digits.

However:


If the number is divisible by \$\lfloor b÷2+1\rfloor\$ (rounded down, e.g base 7 would be 7/2=3.5, 3.5+1=4.5, rounded to 4), then output 'Fizz' instead of the number.
If the number is divisible by \$\lceil b÷3+3\rceil\$ (rounded up, e.g 11/3=3.666, 3.666+3=6.666, rounded to 7), then output 'Buzz'.
As you can probably guess, if your number is divisible by both, output 'Fizzbuzz'.


Examples

Using [0-9], [A-Z] and [a-z] as the digits

(I've only included the first 10 values to keep the examples short - normally there'd by 4990 more items in each sequence)

Input: 10 (so 'Fizz' = 6 and 'Buzz' = 7)

Output: 1, 2, 3, 4, 5, Fizz, Buzz, 8, 9, 10

Input: 2 (so 'Fizz' = 2 and 'Buzz' = 4)

Output: 1, Fizz, 11, Fizzbuzz, 101, Fizz, 111, Fizzbuzz, 1001, Fizz

(I've included the first 50 values of the following to better show how they work)

Input: 55 (so 'Fizz' = \$28_{10}\$ = \$s_{55}\$ and 'Buzz' = \$22_{10}\$ = \$m_{55}\$)

Output: 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, g, h, i, j, k, l, Buzz, n, o, p, q, r, Fizz, t, u, v, w, x, y, z, A, B, C, D, E, F, G, H, I, J, K, L, M, N

Rules


Standard loopholes are forbidden
This is Code Golf, so shortest answer in bytes wins
Input and output can be through console, or function arguments/returns
Leading/trailing white space is fine, as are empty lines
Spaces between 'Fizz' and 'Buzz' are disallowed
Any capitalization variant of 'Fizz'/'Buzz'/'Fizzbuzz' is fine.
Outputs should be separated by newlines.
If you return a array of base 10 'digits' instead of representing them with characters, then they have to be in the correct order!
JavaScript (ES6),  117  116 bytes
Outputs comma-delimited digits, each digit being expressed as a decimal quantity (e.g. \$19_{20}\$ is \$19\$ and \$21_{20}\$ is \$1,1\$).
b=&gt;(g=n=&gt;n&gt;1?g(n-1)+`
`+((s=n%(b+2&gt;&gt;1)?'':'Fizz',n%(b/3+3.9|0)?s:s+'Buzz')||(g=n=&gt;n?[...g(n/b|0),n%b]:s)(n)):1)(5e3)

Try it online!
(limited to 100 so that TIO's output does not blow up)