Subset Sum Possibility

You are given n villagers each possessing a certain number of gold coins, along with a dragon that demands exactly k coins. Your task is to determine whether it is possible to select a subset of villagers such that the sum of their coins is exactly k.

Formally, given a list of integers \(a_1, a_2, \dots, a_n\) representing the number of coins each villager has, determine if there exists a subset \(S\) such that:

\(\sum_{i \in S} a_i = k\)

If such a subset exists, output "Possible"; otherwise, output "Impossible".

inputFormat

The input consists of three lines:

• The first line contains a single integer n, denoting the number of villagers.
• The second line contains n space-separated integers, where each integer represents the number of gold coins that a villager has.
• The third line contains a single integer k, the exact number of coins required by the dragon.

outputFormat

Output a single line containing either "Possible" if there exists a subset that sums to exactly k or "Impossible" if no such subset exists.

## sample

5
3 34 4 12 5
9

Possible

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