Embedding Between $L^p[a,b]$ is not compact

Question

I know that for 1$\leq q\leq p<\infty$, there is an inequality $\|f\|_{L^q}\leq (b-a)^{(1/q)-(1/p)}\|f\|_{L^p}$. So $L^p[a,b]$ can be embedded into $L^q[a,b]$. The embedding seems to be obviously not compact, i.e. there is an bounded sequence $\{x_n\}\subset L^p[a,b]$, $\{x_n\}$ has no convergent subsequence in $L^q[a,b]$. But I get stuck finding such a counterexample. Any hint will help.