$(8$ points$)$ Let $L$ be the language of all binary strings of even length that have a $1$ somewhere in the second

half of the string. $($Formally$,$ letting $$:$=\{0,1\},$

$\{$:$L$:$=\{x1y$:$x,$yin${}^{**}$&$|x|>|y|$&$|x1y|is$ even $\}).$

Fill in the two blanks in the following proof via the Pumping Lemma for regular languages that $L$ is not

pumpable $($hence not regular$)$:

"Given any $p>0,$ let $s$:$=xP|yP.$ Clearly, $sinL$ and $|s|p.$