$ 1^k+2^k+3^k+...+(p-1)^k $ always a multiple of $p$?

Question

I would appreciate if somebody could help me with the following problem:

Q: For any prime number $p(p\geq 3), k=1,2,3,...,p-2$, why is $$ 1^k+2^k+3^k+...+(p-1)^k $$ always a multiple of $p$ ?