How to generate between 1 and n random numbers (positive integers greater than 0) which sum up to exactly n?

Example results if n=10:

10
2,5,3
1,1,1,1,1,1,1,1,1,1
1,1,5,1,1,1

Each of the permutations should have the same probability of occurring, however, I don't need it to be mathematically precise. So if the probabilities are not the same due to some modulo error, I don't care.

Is there a go-to algorithm for this? I only found algorithms where the number of values is fixed (i.e., give me exactly m random numbers which sum up to n).