Does solution for (n,k) (19,18) exist?
I only find the answer for (21,18).
Do you guy have a better idea?

31
2 1
4 3
3 1
1 5
7 6
6 5
5 1
1 5
9 8
8 5
5 10
12 11
11 10
10 5
5 1
1 5
13 10
10 5
5 14
16 15
15 14
14 5
5 14
18 17
17 14
14 19
21 20
20 19
19 14
14 5
5 1

turns out n=19
you can reach state (10,9) and get to (1,18)
this problem has the very beautiful soln. thanks to author.