Find context$-$free grammars for the following languages $($with $n0,m0,k$

$0$

$($a$)L=\{a^n{b}^m$:$nm+1\}.($Hint: $n-m=0$ or $1,$ or $n-m<mn\; id="EditorElement\_856093">0</mn><mtext\; id="EditorElement\_856075"></mtext><mi\; id="EditorElement\_856076">)</mi>$

$($b$)L=\{a^n{b}^m{c}^k$:$k=n+m\}.($Hint: take advantage of the pattern $x^n{y}^n)$