Solve the programming task below in a Python markdown code block.
Read problems statements in [Mandarin Chinese], [Russian], [Vietnamese], and [Bengali] as well.

Chef has a *tasty ingredient* ― an integer $K$. He defines a *tasty matrix* $A$ with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$) as $A_{i, j} = K + i + j$ for each valid $i,j$.

Currently, Chef is busy in the kitchen making this tasty matrix. Help him find the bitwise XOR of all elements of this matrix.

------  Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first and only line of each test case contains three space-separated integers $N$, $M$ and $K$.

------  Output ------
For each test case, print a single line containing one integer ― the bitwise XOR of all elements of the tasty matrix with the given dimensions made with the given special ingredient. 

------  Constraints ------
$1 ≤ T ≤ 10^{5}$
$1 ≤ N, M ≤ 2 \cdot 10^{6}$
$1 ≤ K ≤ 10^{9}$
the sum of $N$ over all test cases does not exceed $2 \cdot 10^{6}$
the sum of $M$ over all test cases does not exceed $2 \cdot 10^{6}$

----- Sample Input 1 ------ 
2

2 2 5

2 3 7
----- Sample Output 1 ------ 
14

5
----- explanation 1 ------ 
Example case 1: The matrix is
$$A = \begin{pmatrix}
5 + 1 + 1 & 5 + 1 + 2\\
5 + 2 + 1 & 5 + 2 + 2\end{pmatrix}
= \begin{pmatrix}
7 & 8 \\
8 & 9 
\end{pmatrix} \,.$$

The XOR of all its elements is $7 \oplus 8 \oplus 8 \oplus 9 = 14$.

Example case 2: The matrix is
$$A = \begin{pmatrix}
7 + 1 + 1 & 7 + 1 + 2 & 7 + 1 + 3\\
7 + 2 + 1 & 7 + 2 + 2 & 7 + 2 + 3
\end{pmatrix}
= \begin{pmatrix}
9 & 10 & 11\\
10 & 11 & 12
\end{pmatrix} \,.$$

The XOR of all its elements is $9 \oplus 10 \oplus 11 \oplus 10 \oplus 11 \oplus 12 = 5$.