Shuffle An Array So That No Element Moves More Than K Places

I have an array, and I'd like to shuffle the array so that no element moves more than K places from its initial position in the array. So for example, if K is 2, and the original array is:

[1,2,3,4,5,6,7,8]

this is a valid permutation:

[1,3,2,5,4,8,6,7]

but this is not:

[1,2,5,4,6,8,3,7]

because the 3 has moved 4 places.

Is there a way to do this so that it's a perfectly random shuffle (in other words, all permutations that satisfy this criteria are equally likely?)