inverse

Time Limit: 8000/4000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 193    Accepted Submission(s): 97

Problem Description

Mike has got a huge array b, and he is told that the array is encrypted.

The array is encrypted as follows.

Let ai(0≤i<n) be the i-th number of this original array.

Let bi(0≤i<n) be the i-th number of this encrypted array.

Let n be a power of 2, which means n=2k.

The bi is calculated as following.

bi=∑0≤j<nf((i or j) xor i)aj

f(x) means, if the number of 1 in the binary of x is even, it will return 1, otherwise 0.

Mike want to inverse the procedure of encryption.

Please help him recover the array a with the array b.

Input

The first line contains an integer T(T≤5), denoting the number of the test cases.

For each test case, the first line contains an integer k(0≤k≤20),
The next line contains n=2k integers, which are bi respectively.

It is guaranteed that, ai is an integer and 0≤ai≤109.

Output

For each test case, output ‘‘Case #t:‘‘ to represent this is the t-th case. And then output the array a.

Sample Input

2
0
233
2
5 3 4 10

Sample Output

Case #1: 233
Case #2: 1 2 3 4

Source

The 2015 ACM-ICPC China Shanghai Metropolitan Programming Contest

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