Getting N random numbers that the product is M

I have have a constrain where the product of random variables is equal to M. The random variables are independent uniform variables between 0 and 1.

I want to get N random numbers that the product of them is a value M.

For example, let's suppose I want 5 random numbers have the product equal to 1

Then, a valid possibility is:

0.2 0.2 0.2 0.2 0.2

Other possibility is:

0.8 0.1 0.03 0.03 0.04

And so on. How would a solution to this look like?