In $$\triangle ABC, \angle ABC = 45^\circ, \angle CAB = 30^\circ$$ and CD is perpendicular to AB. If CD = 100, then AB =

A

$$100 \left(\sqrt{3} + 1\right)$$

B

$$100 \left(\sqrt{3} - 1\right)$$

C

$$50 \left(\sqrt{3} + 1\right)$$

D

$$50 \left(\sqrt{3} - 1\right)$$