I explain: you have to modify Dijkstra in a way that it never finds a path from S to D of length equal to "L".

Dijkstra(S, D, L) // finds path from S to D not equal to L

It's easy to implement: when you relax distances, you firstly check if the node you're relaxing is D and the distance found is equal to L, if it is, you don't relax! (If "X" is the absolutely minimal distance, you will necessarily find a path greater than X, if it exists).

Then do this way:

Min_dist = Integer.MAX_VALUE

For i=1 to K

....Min_dist = Dijkstra(S, D, Min_dist);

When i=1 the call to Dijkstra returns the absolute minimal distance (it never finds a path of length "Integer.MAX_VALUE"). Next times, it must find only lengths greater than "Min_dist".