Cookie Preparation Problem

You are given two integers N and M. You need to determine whether it is possible to prepare exactly N different types of cookies using M available ingredients. Each cookie type is made by selecting a non‐empty subset of the ingredients.

Note that with M ingredients, the total number of unique non-empty combinations is given by the formula: $$2^M - 1$$. If N is less than or equal to this total number, then it is possible to obtain exactly N distinct cookie types; otherwise, it is impossible.

inputFormat

The input consists of a single line containing two space-separated integers N and M.

• N: The number of different cookie types needed.
• M: The number of available ingredients.

outputFormat

Output a single line containing either Possible if it is feasible to prepare exactly N different types of cookies, or Impossible otherwise.

5 3

Possible