[Solution] Find A, B, C CodeChef Solution | Codechef Solution

[Solution] Find A, B, C CodeChef Solution | Codechef Solution

Chef has 3$3$ hidden numbers A,B,$A,B,$ and C$C$ such that 0≤A,B,C≤N$0\le A,B,C\le N$.

Let f$f$ be a function such that f(i)=(A⊕i)+(B⊕i)+(C⊕i)$f(i)=(A\oplus i)+(B\oplus i)+(C\oplus i)$. Here ⊕$\oplus$ denotes the bitwise XOR operation.

Given the values of f(0),f(1),…,f(N)$f(0),f(1),\dots ,f(N)$, determine the values of A,B,$A,B,$ and C$C$.

It is guaranteed that at least one tuple exists for the given input. If there are multiple valid tuples of A,B,C$A,B,C$, print any one.

Input Format

• The first line of input will contain a single integer T$T$, denoting the number of test cases.

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• Each test case consists of multiple lines of input.
  • The first line of each test case contains a single integer N$N$ denoting the upper bound on the values of A,B,C$A,B,C$.
  • Next line contains N+1$N+1$ space-separated integers denoting f(0),f(1),…,f(N)$f(0),f(1),\dots ,f(N)$.

Output Format

For each test case, output on a new line, three space-separated integers, the values of A,B,$A,B,$ and C$C$.

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 If there are multiple valid tuples of A,B,C$A,B,C$, print any one.

Constraints

• 1≤T≤2⋅104$1\le T\le 2\cdot {10}^4$
• 2≤N≤105$2\le N\le {10}^5$
• Sum of N$N$ over all test cases does not exceed 2⋅105