How would you convert acetic acid to methyl amine?

Complete the following equation by writing the structures of A, B and C.

${\mathrm{CH}}_3\mathrm{COOH} \stackrel{{\mathrm{Cl}}_2/\mathrm{P}}{\to } \mathrm{A} \stackrel{\mathrm{NaCN}}{\to } \mathrm{B} \underset{{\mathrm{H}}^{+}}{\overset{{\mathrm{H}}_2\mathrm{O}}{\to }} \mathrm{C}$

Identify A, B and C from the following: 

${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH} \stackrel{{\mathrm{PCl}}_5}{\to } \left(\mathrm{A}\right) \stackrel{\mathrm{KCN}}{\to } \left(\mathrm{B}\right) \stackrel{{\mathrm{H}}_3{\mathrm{O}}^{+}}{\to } \left(\mathrm{C}\right)$.