A permutation is an ordered arrangement of objects. For example, $ 3124 $ is one possible permutation of the digits $ 1, 2, 3 $ and $ 4 $. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of $ 0, 1 $ and $ 2 $ are:
What is the millionth lexicographic permutation of the digits $ 0, 1, 2, 3, 4, 5, 6, 7, 8 $ and $ 9 $?