Box Packing Problem

You are given a set of products and a set of boxes. Each product has a weight and each box has a weight limit. Your task is to determine if it is possible to pack all the products into the boxes such that no box exceeds its weight limit.

For a valid packing, the total weight of products must satisfy the inequality:

[ \sum_{i=1}^{N} w_i \le \sum_{j=1}^{M} L_j ]

where \(w_i\) represents the weight of the \(i\)-th product and \(L_j\) represents the weight limit of the \(j\)-th box. In addition, you can pack at most one product into one box in each step according to a greedy strategy. Decide whether a valid packing exists.

If it is possible, output Possible, otherwise output Impossible.

inputFormat

The input is read from stdin and has the following format:

• The first line contains a single integer T which denotes the number of test cases.
• For each test case, the input is given in four lines:
  • The first line contains an integer N denoting the number of products.
  • The second line contains N space-separated integers representing the weights of the products.
  • The third line contains an integer M denoting the number of boxes.
  • The fourth line contains M space-separated integers representing the weight limits of the boxes.

outputFormat

For each test case, output a single line to stdout containing either Possible if the products can be successfully packed into the boxes under the given constraints or Impossible otherwise.

## sample

3
5
10 20 10 30 40
3
50 50 30
4
15 35 25 10
3
20 30 40
3
5 10 20
2
15 25

Possible
Impossible
Possible

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