Nonzero solutions

Logic Level 3

A B C + E F G H I J K \begin{array}{ccccc} & A& B &C \\ + & E& F &G \\ \hline H & I& J &K\\ \hline \end{array}

Above shows a cryptogram. How many solutions for H I J K \overline{HIJK} are there, such that no digits of H I J K \overline{HIJK} is 0? For example: 1234

Note: No digit is negative.

5 0 2 4 3 1

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