IR-MO 2003 Problem 5

Let $p$ be an odd prime number. Let $S$ be the sum of all primitive roots modulo $p$ . Show that if $p-1$ isn't squarefree (i. e., if there exist integers $k$ and $m$ with $k>1$ and $p-1=k^2m$ ), then $S \equiv 0 \mod p$ .

If not, then what is $S$ congruent to $\mod p$ ?