CF2130B Pathless

There is an array $ a_1, a_2, \ldots, a_n $ consisting of values $ 0 $ , $ 1 $ , and $ 2 $ , and an integer $ s $ . It is guaranteed that $ a_1, a_2, \ldots, a_n $ contains at least one $ 0 $ , one $ 1 $ , and one $ 2 $ . Alice wants to start from index $ 1 $ and perform steps of length $ 1 $ to the right or to the left, and reach index $ n $ at the end. While Alice moves, she calculates the sum of the values she is visiting, and she wants the sum to be exactly $ s $ . Formally, Alice wants to find a sequence $ [i_1, i_2, \ldots, i_m] $ of indices, such that: - $ i_1 = 1 $ , $ i_m = n $ . - $ 1 \leq i_j \leq n $ for all $ 1 \le j \le m $ . - $ |i_{j} - i_{j+1}| = 1 $ for all $ 1 \leq j < m $ . - $ a_{i_1} + a_{i_2} + \ldots + a_{i_m} = s $ . However, Bob wants to rearrange $ a_1, a_2, \ldots, a_n $ to prevent Alice from achieving her target. Determine whether it is possible to rearrange $ a_1, a_2, \ldots, a_n $ such that Alice cannot find her target sequence (even if Alice is smart enough). If it is possible, you also need to output the rearranged array $ a_1, a_2, \ldots, a_n $ .

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^3 $ ). The description of the test cases follows. The first line of each test case contains two integers $ n $ and $ s $ ( $ 3 \le n \le 50 $ , $ 0 \le s \le 1000 $ ). The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \le a_i \le 2 $ ). It is guaranteed that $ a $ contains at least one $ 0 $ , one $ 1 $ , and one $ 2 $ .

For each test case, if it is possible to rearrange $ a $ such that Alice cannot find her target sequence, output $ n $ integers — such rearrangement of $ a $ . Otherwise, output $ -1 $ instead.

In the first test case, any rearrangement of $ a $ can prevent Alice from achieving her target. In the second test case, regardless of rearranging $ a $ , Alice can always find the sequence $ [1,2,3] $ as her target sequence. In the third test case,there is no rearrangement of $ a $ that can prevent Alice from achieving her target. For example, for $ a=[0,2,1] $ , Alice can find the sequence $ [1,2,3,2,3] $ as her target sequence.