P13137 [HackerEarth] mirrors and trees
普及
题目描述

Given a binary tree in a two dimensional plane which has both side covered by mirrors.
As this is a 2D dimensional image, we define our print function to print only those nodes whose reflection is showing
on one of the mirrors, first we print the value of the nodes with reflections appearing on the right mirror and then print
the values of the ones appearing on the left and we don't need to print the same node again which has already been
printed on right mirror, so each node is going to printed only once even in a case where the node has a reflection on
both mirrors.

Suppose in the array representation of binary trees, we fill the positions where the left or right child of a node does not exist with 0s.
So the tree
3
/
2
/
1
will look in array representation as 3 2 0 1 0 0 0 0 0 0 0 0 0 0 0 i.e.
3
/ \
2 0
/ / \
1 0 0 0
/ / / / \
0 0 0 0 0 0 0 0

and the tree

    1 
   /   
  2   3

will look in the array representation as 1 2 3 0 0 0 0 i.e.
1
/
2 3
/ /
0 0 0 0

here for every ith node, it's left child is at (2 * i) th and right child at (2 * i + 1)th position.

Input:
First line contains number of test cases T. First line of each test case contains a single integer N,size of array and second line contains the tree in array representation form as mentioned above.

Output:
For each test case, first print the value of the nodes with reflections appearing on the right mirror and then print values of the ones appearing on the left and
don't need to print the same node again which has already been printed on right mirror, so each node is going to printed only once even in a case where the node has a reflection on
both mirrors.

Constraints:
1 ≤ T ≤ 20
3 ≤ N ≤ 2^18
0 ≤ **A^i ≤ 1000000

Note:
The value of N will always be greater than equal to 3 and will be in the form (2^k-1) where k ≥ 2.
Last level of the tree is filled with all 0s.
Assume array indices start from 1.

SAMPLE INPUT
2
7
1 2 3 0 0 0 0
7
1 3 0 0 0 0 0SAMPLE OUTPUT
1
3
2

1
3

输入格式

见题面

输出格式

见题面

样例输入
20 511 4 114 122 119 120 102 114 70 73 83 66 47 53 48 45 77 90 33 34 93 77 15 21 97 103 58 59 33 51 34 37 113 134 94 77 112 128 76 84 98 122 40 33 42 43 43 47 0 0 108 121 42 49 68 95 106 124 87 103 15 38 0 0 33 69 88 81 33 41 55 50 63 62 19 24 30 30 58 57 88 112 94 109 50 72 45 29 87 111 55 44 101 124 82 69 0 0 0 0 34 28 74 101 33 34 97 104 50 77 32 29 68 48 85 64 73 66 64 71 39 39 32 31 0 0 0 0 65 71 75 82 44 70 34 36 0 0 30 57 37 65 102 122 65 52 56 34 57 57 65 39 33 13 98 126 24 22 44 67 120 103 30 56 35 40 96 89 57 80 23 12 60 71 58 52 55 67 34 33 7 27 59 56 47 25 39 52 25 11 73 96 0 0 0 0 0 0 0 0 77 63 39 56 90 108 75 83 92 95 105 98 0 0 111 118 63 73 89 84 53 31 51 45 89 93 23 44 98 87 41 25 69 76 23 38 28 40 74 88 39 21 24 16 58 66 46 59 0 0 0 0 0 0 0 0 113 85 0 0 52 59 82 86 105 125 76 76 42 23 51 76 0 0 0 0 119 103 120 112 36 32 70 60 109 113 77 92 83 80 98 90 29 46 15 48 36 51 25 29 86 87 87 98 91 111 105 107 62 77 47 42 115 98 55 56 7 29 127 128 17 7 121 110 102 119 122 125 67 94 75 62 75 89 48 56 59 91 117 101 42 68 24 5 66 87 57 66 42 55 52 57 0 0 70 94 69 61 29 12 0 0 107 118 98 116 54 75 103 104 96 102 74 62 21 19 91 112 52 33 102 88 31 44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 20 61 85 7 7 111 127 98 105 108 101 52 83 101 121 29 27 58 66 22 23 79 104 0 0 0 0 67 76 61 42 55 49 111 102 17 16 53 57 36 43 97 102 91 83 91 122 62 89 30 49 47 44 113 122 59 71 69 78 37 27 86 98 81 105 75 93 94 110 27 53 0 0 99 123 33 49 65 71 104 100 33 19 41 68 13 25 40 29 85 82 103 94 11 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 511 3 87 84 0 0 29 42 0 0 0 0 47 55 9 15 0 0 0 0 0 0 0 0 66 50 36 50 80 85 72 107 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 28 100 113 108 100 100 107 68 58 43 31 68 71 40 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 112 121 43 47 77 67 44 40 29 28 60 52 99 101 16 26 49 63 98 85 16 34 19 10 125 125 28 47 91 100 107 82 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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