[Solution] Equal by XORing CodeChef Solution | CodeChef Problem Solution 2022

[Solution] Equal by XORing CodeChef Solution | CodeChef Problem Solution 2022

JJ has three integers A$A$, B$B$, and N$N$. He can apply the following operation on A$A$:

• Select an integer X$X$ such that 1≤X<N$1\le X<N$ and set A:=A⊕X$A:=A\oplus X$. (Here, ⊕$\oplus$ denotes the bitwise XOR operation.)

JJ wants to make A$A$ equal to B$B$.
Determine the minimum number of operations required to do so. Print −1$-1$ if it is not possible.

Input Format

• The first line contains a single integer T$T$ — the number of test cases. Then the test cases follow.

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• The first and only line of each test case contains three integers A$A$, B$B$, and N$N$ — the parameters mentioned in the statement.

Output Format

For each test case, output the minimum number of operations required to make A$A$ equal to B$B$.

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 Output −1$-1$ if it is not possible to do so.

Constraints

• 1≤T≤1000$1\le T\le 1000$
• 0≤A,B<230$0\le A,B<2^{30}$
• 1≤N≤230