KVPY #3

Suppose that $a_2, a_3, a_4, a_5, a_6, a_7$ are integers such that $\frac57=\frac{a_2}{2!}+\frac{a_3}{3!}+\frac{a_4}{4!}+\frac{a_5}{5!}+\frac{a_6}{6!}+\frac{a_7}{7!},$ where $0 \leq a_j < j$ for $j=2, 3, 4, 5, 6, 7.$

What is the sum $a_2+a_3+a_4+a_5+a_6+a_7?$

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Notation: $!$ is the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .