A job has been assigned to Jar Jar Binks, it goes as follows:

There are N spaceships parts, each with a weight of Wi kg. Given a weight W, he has to show how many parts can be used in order to make a ship with a weight of exactly W kg. He has to show all possible solutions, of course if possible.

Everybody knows Jar Jar Binks particularly because of his clumsiness, so you have to help him. Write a program that solves his problem!

Input

There will be several cases, each beginning with two integers N, Q (1 ≤ N ≤ 60, 0 ≤ Q ≤ 10000).

Next there will be N positive integers representing the weights of the N spaceship parts (1 ≤ Wi ≤ 1000).

Q lines will follow, each one with only one (not necessarily positive) integer W, the total weight of the spaceship.

End of input will be denoted with N = 0 and Q = 0. This case should not be processed.

Output

Print a line with K integers per query in ascending order. They must represent the amount of pieces that can be used to make a spaceship with weight W.

If there is no way to make a spaceship with weight W, output a line with the string “That's impossible!” (quotes to clarify)

Example

Input:
5 4
1 2 3 1 1
3
5
1
9
0 0

Output:
1 2 3
2 3 4
1
That's impossible!

Explanation of the query W = 5

A spaceship with weight = 5 kg can be formed with 2, 3 and 4 parts, for example:

• 2 kg + 3 kg = 5 kg
• 3 kg + 1 kg + 1 kg = 5 kg
• 1 kg + 1 kg + 1 kg + 2 kg = 5 kg