What is wrong with the following (faulty) "proof" that LHALT E NP? "Proof". Define verifier V((M), x), k): (a) Run M on input r for up to k steps. (b) If M halts within these k steps, accept; otherwise, reject If (M), x) LHALT, then M must halt on x after some finite number of steps k, which means that V(((M), x), K) will accept. And if M), x) LHALT, then V t certificate k is provided. Therefore, V is an efficient verifier for LHALT, SO LHALT E NP. D will reject no matterwha What is wrong with the following (faulty) "proof" that LHALT E NP? "Proof". Define verifier V((M), x), k): (a) Run M on input r for up to k steps. (b) If M halts within these k steps, accept; otherwise, reject If (M), x) LHALT, then M must halt on x after some finite number of steps k, which means that V(((M), x), K) will accept. And if M), x) LHALT, then V t certificate k is provided. Therefore, V is an efficient verifier for LHALT, SO LHALT E NP. D will reject no matterwha