Given a list of values z₀, z₁, . . . ,z_n-1 (possibly with repetitions), show how to find the coefficients of a polynomial P(x) of degree-bound n + 1 that has zeros only at z₀, z₁, . . . ,z_n-1  (possibly with repetitions). Your procedure should run in time O(n lg² n). The polynomial P(x) has a zero at z_j if and only if P(x) is a multiple of (x − z_j).)