If $\lim _{x \rightarrow a^{+}} f(x)=p, \lim _{x \rightarrow a^{-}} f(x)=m$ and $f(a)=k$,then which one of the following is true?

• A
  When $p-k \neq 0$ and $m-k \neq 0$,then $f(x)$ is continuous at $x=a$
• B
  When $p-k=0$ and $m-k \neq 0$,then $f(x)$ is left continuous at $x=a$
• C
  When $p-k \neq 0$ and $m-k=0$,then $f(x)$ is right continuous at $x=a$
• D
  When $p-m=0$ and $p-k=0$,then $f(x)$ is continuous at $x=a$