Consider the following languages A $=\{<$ M $,$ k $>|$ M is a TM that accepts all strings of length less than k $\}$ and A $=\{<$ M $,$ k $>|$ M is a TM that accepts some strings of length less than k $\}$ Note the difference between the languages all strings vs some strings. We want to show that A $$ is recognizable. We have shown that A $$ is recognizable $($you can find the solution under the final exam study guide $).$ Explain why the TM used to show A $$ is recognizable does not work for A $?$ How do you modify it to get a TM to recognize A $.$