Mongolian Mathematical Olympiad

Let $m>2$ be a natural number and if $i\ne j$ then $a_i\ne a_j(\mathrm{mod}m)$. Prove that if $(a_i,m)=1$, $i=1,\phi (m)$ then there exists the permutation $b_1,b_2,...,b_{\phi (m)}$ of numbers $a_1,a_2,...,a_{\phi (m)}$ such that $a_1^{b_1}+a_2^{b_2}+...+a_{\phi (m)}^{b_{\phi (m)}}$ is divisible by $m$.