Write a function f(n,k) that displays the k-dimensional countdown from n.
A 1-dimensional countdown from 5 looks like
54321
A 2-dimensional countdown from 5 looks like
54321
4321
321
21
1
Finally, a 3-dimensional countdown from 5 looks like
54321
4321
321
21
1
4321
321
21
1
321
21
1
21
1
1
Formal definition
The 1-dimensional countdown from any n is a single line with the digits n, n-1,...,1 concatenated (followed by a newline).
For any k, the k-dimensional countdown from 1 is the single line
1
For n > 1 and k > 1, a k-dimensional countdown from n is a (k-1)-dimensional countdown from n followed by a k-dimensional countdown from n-1.
Input
Two positive integers k and n <= 9, in any format you choose.
Output
The k-dimensional countdown from n, with a newline after each 1-dimensional countdown. Extra newlines are permitted in the output.
Edit: Digits on a line do not need to be adjacent, but they must be evenly-spaced.
Scoring
Standard golf scoring.
Bonus example
Here's an example with k > n, a 4-dimensional countdown from 3 (with extra comments that are not to be included in actual solutions):
-- 3-dimensional countdown from 3
321
21
1
21
1
1
-- 4-dimensional countdown from 2:
---- 3-dimensional countdown from 2:
21
1
1
---- 4-dimensional countdown from 1:
1
Clarifications:
Digits on a line do not need to be adjacent, but they must be evenly-spaced.
You may write a full program instead of just a function, if you prefer.