# Convolution Of Step function

I am trying to see if I understand the convolution process correctly.
This is from the solved example of my prof's notes:

x[n] = u[n]
and h[n] = a-nu[-n] for 0<a<1

As expected the first step was

y[n] = x[n]* h[n]

= Ʃ h[k]x[n-k] -∞<k<∞
= Ʃ a-ku[-k]u[n-k] -∞<k<∞

From my understanding u[-k] = 0 for all k > 0 so that would give us the upper limit of k to be 0
And we would also need for n-k > 0 and when we have those conditions we would just then be left with the summation of a^-k since the other 2 would always evaluate to 1 in that interval.

But for the solution the cases considered were when n <= 0 and when n >0 and then the answers were

Ʃ ak -n<k<∞ for the first case (n<=0)
and Ʃak 0<k<∞

I dont understand how they came to those intervals. Any help would be appreciated.