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.For each test case, output ‘‘Case #t:‘‘ to represent this is the t-th case. And then output the array a.
Case #1: 233
Case #2: 1 2 3 4
