k-th permutation of n elements [a b c d ... ]

idx1 = int(k/(n-1)!)
k = k % (n-1)!

idx2 = int(k/(n-2)!)
k = k % (n-1)!

idx3 = int(k/(n-3)!)
k = k % (n-1)!

...

idxn = ...

Then extract the element idx1 from the array of elements (it results in a new array)
From the new array pick the idx2 element
And so on