Clock With Permutated Hours

We have an analog clock with hour-numbers which are not glued on. An army of ants moves some of the numbers around every hour. At hour k, the ants move the numbers currently at positions (k+1) through (k+a(k)) (taken mod 12) one position counterclockwise each. And the ants move the number at position k to position (k+a(k)).

(Position j is where j-o'clock normally is on an unaltered clock.)

Now, each a(k) is an integers such that 1 <= a(k) <= 5.

After 12 hours, the clock numbers are arranged like this:

1 12 3 2 11 6 9 10 5 7 4 8

What is at least one set of a(k)'s which gives this number-arrangement? (I do not know how many solutions there are.)

thanks, Leroy Quet

An exhaustive computer search gives the following two sequences of a(k)'s:

(2, 2, 1, 2, 3, 2, 4, 5, 3, 2, 4, 3) and (2, 2, 1, 2, 3, 2, 4, 5, 4, 2, 4, 2).

It would be interesting to know how many possible arrangements there are, as a function of the upper bound to the a(k)'s. Obviously, if the upper bound is 1 (i.e. 1 <= a(k) <= 1), then there is only one possible arrangement. Is it possible to reach any arrangement if the upper bound is high enough? (An upper bound of 5 is definitely too small, since 5^12 < 12!.)