Consider the function pad : * N * # * that is defined

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Consider the function pad : Σ* × N → Σ*#* that is defined as follows. Let pad(s, l) = s#j , where j = max(0, l−m) andm is the length of s. Thus, pad(s, l) simply adds enough copies of the new symbol # to the end of s so that the length of the result is at least l. For any language A and function f : N → N, define the language pad(A, f) as

pad(A, f) = {pad(s, f(m))| where s ∈ A and m is the length of s}.

Prove that if A ∈ TIME(n6), then pad(A, n2) ∈ TIME(n3).

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