Generate N random numbers within a range with a constant sum

Question

I want to generate N random numbers drawn from a specif distribution (e.g uniform random) between [a,b] which sum to a constant C. I have tried a couple of solutions I could

Answer 1

Although this was old topic but I think I got a idea. Consider we want N random number which sum is C and each random between a and b. To solve problem, we create N holes and prepare C balls, for each time we ask each hole "Do you want another ball?". If no, we pass to next hole, else, we put a ball into the hole. Each hole has a cap value: b-a. If some hole reach the cap value then always pass to next hole.

Example:
3 random numbers between 0 and 2 which sum is 5.

simulation result:
1st run: -+-
2nd run: ++-
3rd run: ---
4th run: +*+
final:221

-:refuse ball
+:accept ball
*:full pass