For any non-empty sequence of positive integers s1, s2, ..., sK their least common multiple is the smallest positive integer that is divisible by each of the given numbers. We will use "lcm" to denote the least common multiple. For example, lcm(3) = 3, lcm(4,6) = 12, and lcm(2,5,7) = 70.
You are given an array S and an integer x. Find out whether we can select some elements from S in such a way that their least common multiple will be precisely x. Formally, we are looking for some s1, s2, ..., sK, K >= 1, such that each si belongs to S, and x=lcm(s1, s2, ..., sK). Return "Possible" if such elements of S exist, and "Impossible" if they don't.