If \(x^xy^y=\dfrac{24^3}2,\) and \(x\) and \(y\) are integers such that \(x < y,\) what is the value of \(y - x?\)

[Gmat_mission]

If \(x^xy^y=\dfrac{24^3}2,\) and \(x\) and \(y\) are integers such that \(x < y,\) what is the value of \(y − x?\)

(A) \(-1\)
(B) \(1\)
(C) \(3\)
(D) \(5\)
(E) \(7\)

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT