You have to solve the following problem with backtracking. You're given a sequence of 10 positive integers n₁, n₂, n₃ ... n₉, n₁₀ and a positive value K.

To solve this problem you need to print a permutation a₁, a₂, a₃ ... a₁₀ of the numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} such that a₁ * n₁ + a₂ * n₂ + a₃ * n₃ + ... + a₁₀ * n₁₀ = K.

Input

In the first line, a single integer T, the number of test cases.

For each test case there will be two lines:

In the first line, 10 positive integers (1 ≤ n_i ≤ 10^9) separated by spaces.

In the second line, a single positive integer K (1 ≤ K ≤ 10^9).

Output

For each test case print a line with the answer for that test case as following:

Among all the permutations that solve the problem according to the description above, print the lexicographically smallest.

You've to print the permutation in a single line, separating each integer by a simple space.

If no such permutation exists, print a single line with "-1".

Example

Input:
2
1 2 3 4 5 6 7 8 9 10
200
1 2 3 4 5 6 7 8 9 10
100

Output:
2 6 8 9 7 5 4 3 1 0
-1