402792: GYM100883 C Too Many Coins

Your friend has C coins in his pocket, each coin has a value V_i, and you know that he will not need that amount of money, he will only need M.

You want to help him not to carry all these coins, so you decided to tell him to take the coins of specific values, in a way that he will have at least the amount of money he needs.

You will tell him that it will be enough for him if he carried coins of types X₁, X₂, ..., X_n.

Note that if you tell him to carry coins of type X_i, he will carry all the coins with values V_i = X_i.

The first line contains an integer T representing the number of test cases.

Each test case consists of two lines, the first line has two integers C (1 ≤ C ≤ 1000000) and M (1 ≤ M ≤ 10⁹), and the other line contains C integers representing the values of the coins (1 ≤ Vi ≤ 1000000).

For each test case print the types of coins which your friend must carry,if there are multiple solutions, print the solution with the minimum number of types, if there are still multiple solutions print the one which makes your friend carry more money, if there are still multiple solutions print the solution with the bigger types.

print the types in increasing order. If he doesn't have enough money print "Impossible" without the quotations.

3
10 7
1 1 1 1 1 2 2 2 5 4
10 11
1 1 1 1 1 1 1 1 1 1
10 6
1 1 1 1 1 1 2 2 2 3

2 5
Impossible
2