Find the sets of sums I've enjoyed reading this site; this is my first question. Edits are welcome.
Given positive integers \$n\$ and \$m\$, compute all ordered partitions of \$m\$ into exactly \$n\$ positive integer parts, and print them delimited by commas and newlines. Any order is fine, but each partition must appear exactly once.
For example, given \$m=6\$ and \$n=2\$, possible partitions are pairs of positive integers that sum to 6:
1,5
2,4
3,3
4,2
5,1

Note that [1,5] and [5,1] are different ordered partitions. Output should be exactly in the format above, with an optional trailing newline. (EDIT: The exact order of the partitions does not matter). Input/output are via standard code-golf I/O.
Another example output for \$m=7, n=3\$:
1,1,5
1,2,4
2,1,4
1,3,3
2,2,3
3,1,3
1,4,2
2,3,2
3,2,2
4,1,2
1,5,1
2,4,1
3,3,1
4,2,1
5,1,1

The smallest code in bytes after 1 week wins.
Again, please edit if necessary.
Addendum:
@TimmyD asked what size of integer input the program has to support. There is no hard minimum beyond the examples; indeed, the output size increases exponentially, roughly modelled by: lines = \$e^{(0.6282 n - 1.8273)}\$.
n | m | lines of output
2 | 1 | 1
4 | 2 | 2
6 | 3 | 6
8 | 4 | 20
10 | 5 | 70
12 | 6 | 252
14 | 7 | 924
16 | 8 | 3432
18 | 9 | 12870
20 | 10 | 48620
22 | 11 | 184756
24 | 12 | 705432
Pyth, 14 bytes

V^SQEIqsNQj\,N


Try it online: Demonstration or Test Suite

Explanation:

V^SQEIqsNQj\,N   implicit: Q = first input number
  SQ             create the list [1, 2, ..., Q]
    E            read another number
 ^               cartesian product of the list
                 this creates all tuples of length E using the numbers in SQ
V                for each N in ^:
     IqsNQ          if sum(N) == Q:
          j\,N         join N by "," and print