You are given two integer arrays $$$a_0, \ldots, a_{n - 1}$$$ and $$$b_0, \ldots, b_{m - 1}$$$. Each integer among $$$1, \ldots, n + m$$$ is present exactly once among $$$a_0, \ldots, a_{n - 1}, b_0, \ldots, b_{m - 1}$$$.

We perform $$$k$$$ operations on the arrays. Namely, for each integer $$$i$$$ from $$$0$$$ to $$$k - 1$$$ in this order

if $$$a_{i \bmod n} \gt b_{i \bmod m}$$$, we swap $$$a_{i \bmod n}$$$ and $$$b_{i \bmod m}$$$
otherwise, we do nothing

Determine the final state of both arrays after all $$$k$$$ operations are completed.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains three integers $$$n, m, k$$$ ($$$1 \leq n, m \leq 2 \cdot 10^5$$$, $$$0 \leq k \leq 10^{18}$$$).

The second line contains $$$n$$$ integers $$$a_0, \ldots, a_{n - 1}$$$.

The third line contains $$$m$$$ integers $$$b_0, \ldots, b_{m - 1}$$$.

It is guaranteed that the joint sequence $$$a_0, \ldots, a_{n - 1}, b_0, \ldots, b_{m - 1}$$$ is a permutation of integers from $$$1$$$ to $$$n + m$$$.

The sum of $$$n + m$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each testcase, print two lines — the states of the arrays $$$a_0, \ldots, a_{n - 1}$$$ and $$$b_0, \ldots, b_{m - 1}$$$ after the $$$k$$$ operations are performed as described above.

Note

The action sequence for the first example

$$$i$$$	$$$i \bmod n$$$	$$$i \bmod m$$$	comparison	action	array $$$a$$$	array $$$b$$$
0	0	0	$$$3 \gt 1$$$	swap $$$a_0$$$ and $$$b_0$$$	[1, 4]	[3, 5, 2]
1	1	1	$$$4 \lt 5$$$	nothing	[1, 4]	[3, 5, 2]
2	0	2	$$$1 \lt 2$$$	nothing	[1, 4]	[3, 5, 2]
3	1	0	$$$4 \gt 3$$$	swap $$$a_1$$$ and $$$b_0$$$	[1, 3]	[4, 5, 2]
4	0	1	$$$1 \lt 5$$$	nothing	[1, 3]	[4, 5, 2]

Idx	Name	Rating
A	Round Trip	800
B	Make Connected	1700
C	Loyalty	1200
D	Locked Out	2100
E	Left is Always Right	2400
F	SubMST	3000
G	Bitwise And Equals	3500
H	Cycle Sort	3500

Pinely Round 5 (Div. 1 + Div. 2)