7311: CodeChef XORSUB - XOR with Subset
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Description
You have an array of integers A1, A2, ..., AN.
The function F(P), where P is a subset of A, is defined as the XOR (represented by the symbol ⊕) of all the integers present in the subset. If P is empty, then F(P)=0.
Given an integer K, what is the maximum value of K ⊕ F(P), over all possible subsets P of A?
Input
The first line contains T, the number of test cases. Each test case consists of N and K in one line, followed by the array A in the next line.
Output
For each test case, print the required answer in one line.
Constraints
$1 ≤ T ≤ 10$
$1 ≤ K, A_i ≤ 1000$
$1 ≤ K, A_i ≤ 1000$
Sample 1 Input
1
3 4
1 2 3
Sample 1 Output
7
Considering all subsets:
F({}) = 0 ? 4 ? 0 = 4
F({1}) = 1 ? 4 ? 1 = 5
F({1,2}) = 3 ? 4 ? 3 = 7
F({1,3}) = 2 ? 4 ? 2 = 6
F({1,2,3}) = 0 ? 4 ? 0 = 4
F({2}) = 2 ? 4 ? 2 = 6
F({2,3}) = 1 ? 4 ? 1 = 5
F({3}) = 3 ? 4 ? 3 = 7
Therefore, the answer is 7.
F({}) = 0 ? 4 ? 0 = 4
F({1}) = 1 ? 4 ? 1 = 5
F({1,2}) = 3 ? 4 ? 3 = 7
F({1,3}) = 2 ? 4 ? 2 = 6
F({1,2,3}) = 0 ? 4 ? 0 = 4
F({2}) = 2 ? 4 ? 2 = 6
F({2,3}) = 1 ? 4 ? 1 = 5
F({3}) = 3 ? 4 ? 3 = 7
Therefore, the answer is 7.