$[10$ Points$]$ Mapping reductions. Let $\backslash$Sigma $=\{0,1\}.$ Which, if any, of the following languages are mapping$-$reducible to A$\_$TM$?$ Justify your answers: either prove that a mapping reduction exists or prove that none can exist.

$($a$)$ L$1=\{|$ M accepts at least one string consisting only of $1$s$\}$

$($b$)$ L$2=\{|$ M accepts no input$\}$