Chef has an array A of length N and an integer X.

In one operation, Chef does the following:
Find the smallest element in the current array. Let this be S.
Next, pick any one index i such that A_{i} = S
Finally, replace A_{i} with $A_{i} \oplus X$

Here $\oplus$ denotes the [bitwise XOR] operation.

For example, if A = [1, 1, 2] and X = 4, then in one move Chef can turn the array into either [5, 1, 2] or [1, 5, 2].

Chef performs this operation exactly Y times. Let B be final array obtained.

Output the array B in sorted order. Note that under this restriction, the output is unique.

------ Input Format ------

• The first line of input will contain a single integer T, denoting the number of test cases.
• Each test case consists of two lines of input.
• The first line of each test case contains three space-separated integers N, X, and Y.
• The second line contains N space-separated integers denoting the array A.

------ Output Format ------

For each test case, output array B in sorted order.

------ Constraints ------

$1 ≤ T ≤ 10^{4}$
$1 ≤ N ≤ 10^{5}$
$1 ≤ Y ≤ 10^{9}$
$1 ≤ A_{i} , X ≤ 2^{30}$
- The sum of $N$ over all test cases won't exceed $10^{5}$.

----- Sample Input 1 ------
3
1 6 99
9
3 7 44
1 2 3
5 20 6
5 10 15 20 25

----- Sample Output 1 ------
15
3 5 6
5 20 25 27 30

----- explanation 1 ------
Test case $1$: The array is initially $[9]$. Since there is only one element, it will be modified in each step. So,
- After the first operation, the array is $[15]$ (since $9 \oplus 6 = 15$)
- After the second operation, the array is $[9]$ (since $15 \oplus 6 = 9$)
- Continuing the above, it can be verified that after $99$ steps, the array is $[15]$.

Test case $3$: The sequence of steps is as follows:
- Initially, the array is $[5, 10, 15, 20, 25]$
- After operation $1$, it is $[17, 10, 15, 20, 25]$
- After operation $2$, it is $[17, 30, 15, 20, 25]$
- After operation $3$, it is $[17, 30, 27, 20, 25]$
- After operation $4$, it is $[5, 30, 27, 20, 25]$
- After operation $5$, it is $[17, 30, 27, 20, 25]$
- After operation $6$, it is $[5, 30, 27, 20, 25]$

Remember to print the output in sorted order.

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