Given a matrix of m x n and a folding direction, determine what the matrix will look like when folded in the given way.
Given four points on a piece of paper, assume the top left corner has a value of 1, and going in a clockwise direction, each corner increases in value by 1.
Input Format
- The first line is the number of test cases (t)
- The first line of each test case is the size of the matrix (m n)
- The second line of each test case is the folding direction from point c to d
- For the next m lines, each line is the row of that matrix with n values
Constraints
- 1 ≤ c, d ≤ 4 and c ≠ d
- 1 ≤ m, n, t ≤ 1,000,000
- 0 ≤ value inside the matrix (v) ≤ 9
- When folded, if the value of vij that is folded over vi'j' are not the same, we considered it asymmetrical (see Sample 3)
- If a side has the size of 1, we cannot fold perpendicularly to that side.
Output Format
For each test case, print the number of the test case starting with 1 followed by the list the resulting matrix of the folded paper. Use a hyphen symbol (-) for disappearing spaces. If the paper cannot be folded symmetrically, list "error."
Sample Input 1
1
1 1
1 2
0
Sample Output 1
1
error
Sample Output 1 Explanation
The matrix has size 1x1, so it's not foldable.
Sample Input 2
1
3 3
1 3
0 1 2
1 3 1
2 1 0
Sample Output 2
1
--2
-31
210
Sample Output 2 Explanation
If we fold it from corner 1 to corner 3, the numbers match the opposite numbers, so we can fold it symmetrically. The top left part has disappeared, so it is replaced with a hyphen symbol (-) in the output.
Sample Input 3
1
1 2
1 2
5 6
Sample Output 3
1
error
Sample Output 3 Explanation
We have a foldable matrix. However, when we fold from corner 1 to corner 2, the values inside the matrix are different (5 and 6), so we cannot fold it symmetrically.
Sample Input 4
1
1 3
1 2
1 2 1
Sample Output 4
1
-21
Sample Output 4 Explanation
The numbers match each other in the opposite side.
