Rectangular Polyline

Description:

Input:

The first line contains one integer $$$t$$$ ($$$1 \leq t \leq 200$$$) —the number of test cases.

The first line of each test case contains one integer $$$h$$$ ($$$1 \leq h \leq 1000$$$) — the number of horizontal segments. The following line contains $$$h$$$ integers $$$l_1, l_2, \dots, l_h$$$ ($$$1 \leq l_i \leq 1000$$$) — lengths of the horizontal segments of the polyline, in arbitrary order.

The following line contains an integer $$$v$$$ ($$$1 \leq v \leq 1000$$$) — the number of vertical segments, which is followed by a line containing $$$v$$$ integers $$$p_1, p_2, \dots, p_v$$$ ($$$1 \leq p_i \leq 1000$$$) — lengths of the vertical segments of the polyline, in arbitrary order.

Test cases are separated by a blank line, and the sum of values $$$h + v$$$ over all test cases does not exceed $$$1000$$$.

Output:

For each test case output Yes, if there exists at least one polyline satisfying the requirements, or No otherwise. If it does exist, in the following $$$n$$$ lines print the coordinates of the polyline vertices, in order of the polyline traversal: the $$$i$$$-th line should contain two integers $$$x_i$$$ and $$$y_i$$$ — coordinates of the $$$i$$$-th vertex.

Note that, each polyline segment must be either horizontal or vertical, and the segments should alternate between horizontal and vertical. The coordinates should not exceed $$$10^9$$$ by their absolute value.

Sample Input:

2
2
1 1
2
1 1

2
1 2
2
3 3

Sample Output:

Yes
1 0
1 1
0 1
0 0
No

Sample Input:

2
4
1 1 1 1
4
1 1 1 1

3
2 1 1
3
2 1 1

Sample Output:

Yes
1 0
1 1
2 1
2 2
1 2
1 1
0 1
0 0
Yes
0 -2
2 -2
2 -1
1 -1
1 0
0 0

Sample Input:

2
4
1 4 1 2
4
3 4 5 12

4
1 2 3 6
2
1 3

Sample Output:

Yes
2 0
2 3
3 3
3 7
4 7
4 12
0 12
0 0
No

Note:

In the first test case of the first example, the answer is Yes — for example, the following picture illustrates a square that satisfies the requirements:

In the first test case of the second example, the desired polyline also exists. Note that, the polyline contains self-intersections, but only in the endpoints:

In the second test case of the second example, the desired polyline could be like the one below:

Note that the following polyline is not a valid one, since it contains self-intersections that are not endpoints for some of the segments: