The reduction algorithm F in the proof of Lemma 34.6 constructs the circuit C = f (x) based on knowledge of x, A, and k. Professor Sartre observes that the string x is input to F, but only the existence of A, k, and the constant factor implicit in the O(n^k) running time is known to F (since the language L belongs to NP), not their actual values. Thus, the professor concludes that F can’t possibly construct the circuit C and that the language CIRCUIT-SAT is not necessarily NP-hard. Explain the flaw in the professor’s reasoning.