CF1515A Phoenix and Gold

Phoenix has collected $ n $ pieces of gold, and he wants to weigh them together so he can feel rich. The $ i $ -th piece of gold has weight $ w_i $ . All weights are distinct. He will put his $ n $ pieces of gold on a weight scale, one piece at a time. The scale has an unusual defect: if the total weight on it is exactly $ x $ , it will explode. Can he put all $ n $ gold pieces onto the scale in some order, without the scale exploding during the process? If so, help him find some possible order. Formally, rearrange the array $ w $ so that for each $ i $ $ (1 \le i \le n) $ , $ \sum\limits_{j = 1}^{i}w_j \ne x $ .

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In the first test case, Phoenix puts the gold piece with weight $ 3 $ on the scale first, then the piece with weight $ 2 $ , and finally the piece with weight $ 1 $ . The total weight on the scale is $ 3 $ , then $ 5 $ , then $ 6 $ . The scale does not explode because the total weight on the scale is never $ 2 $ . In the second test case, the total weight on the scale is $ 8 $ , $ 9 $ , $ 11 $ , $ 14 $ , then $ 18 $ . It is never $ 3 $ . In the third test case, Phoenix must put the gold piece with weight $ 5 $ on the scale, and the scale will always explode.