Show that the following problem is NP-complete. You are given a set of states Q = {q₀, q₁, . . . , q_l} and a collection of pairs {(s₁, r₁), . . . , (s_k, r_k)} where the s_i are distinct strings over Σ = {0, 1}, and the r_i are (not necessarily distinct) members of Q. Determine whether a DFA M = (Q, Σ, δ, q₀, F) exists where (q₀, s_i) = r_i for each i. Here, (q, s) is the state thatM enters after reading s, starting at state q. Note that F is irrelevant here.