Lexicographic permutations

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:

\[ 012\ \ 021\ \ 102\ \ 120\ \ 201\ \ 210 \]

What is the millionth lexicographic permutation of the digits \( 0 \), \( 1 \), \( 2 \), \( 3 \), \( 4 \), \( 5 \), \( 6 \), \( 7 \), \( 8 \) and \( 9 \)?