SHARYGIN 2014 Problem 9

Two circles $\omega_1$ and $\omega_2$ touching externally at point $L$ are inscribed into angle $BAC$ . Circle $\omega_1$ touches ray $AB$ at point $E$ , and circle $\omega_2$ touches ray $AC$ at point $M$ . Line $EL$ meets $\omega_2$ for the second time at point $Q$ . Prove that $MQ\parallel AL$ .