There are no mountains in Florida, and Florida Man cannot comprehend their existence. As such, he really needs your help with this one.

In the wilderness lies a region of mountainous terrain represented as a rectangular grid with $$$n$$$ rows and $$$m$$$ columns. Each cell in the grid is identified by its position $$$(i, j)$$$, where $$$i$$$ is the row index and $$$j$$$ is the column index. The altitude of cell $$$(i, j)$$$ is denoted by $$$a_{i,j}$$$.

However, this region has been tampered with. A path consisting of $$$n + m - 1$$$ cells, starting from the top-left corner $$$(1, 1)$$$ and ending at the bottom-right corner $$$(n, m)$$$, has been cleared. For every cell $$$(i, j)$$$ along this path, the altitude $$$a_{i,j}$$$ has been set to $$$0$$$. The path moves strictly via downward ($$$\mathtt{D}$$$) or rightward ($$$\mathtt{R}$$$) steps.

To restore the terrain to its original state, it is known that the region possessed a magical property before it was tampered with: all rows and all columns shared the same sum of altitudes. More formally, there exists an integer $$$x$$$ such that $$$\sum_{j=1}^m a_{i, j} = x$$$ for all $$$1\le i\le n$$$, and $$$\sum_{i=1}^n a_{i, j} = x$$$ for all $$$1\le j\le m$$$.

Your task is to assign new altitudes to the cells on the path such that the above magical property is restored. It can be proven that a solution always exists. If there are multiple solutions that satisfy the property, any one of them may be provided.

Input format:
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 two integers $$$n$$$ and $$$m$$$ ($$$2 \leq n, m \leq 1000$$$) — the number of rows and columns in the grid.

The second line of each test case contains a string $$$s$$$ of length $$$n+m-2$$$ ($$$s_i = \mathtt{D}$$$ or $$$s_i = \mathtt{R}$$$) — the steps the path makes from $$$(1, 1)$$$ to $$$(n, m)$$$. The character $$$\mathtt{D}$$$ represents a downward step, and $$$\mathtt{R}$$$ represents a rightward step.

The $$$i$$$-th of the next $$$n$$$ lines each contain $$$m$$$ integers $$$a_{i,1}, a_{i, 2}, \ldots, a_{i,m}$$$ ($$$-10^6 \leq a_{i,j} \leq 10^6$$$) — the altitude of each cell in the grid. It is guaranteed that if a cell $$$(i, j)$$$ lies on the path, then $$$a_{i,j} = 0$$$.

It is guaranteed that the sum of $$$n \cdot m$$$ over all test cases does not exceed $$$10^6$$$.
Output format:
For each test case, output $$$n$$$ lines of $$$m$$$ integers representing the restored grid of altitudes $$$b_{i, j}$$$. The altitudes must satisfy $$$-10^{15} \leq b_{i,j} \leq 10^{15}$$$, and additionally $$$a_{i,j} = b_{i,j}$$$ if $$$(i, j)$$$ is not on the path. If multiple solutions exist, output any of them.
Example Input 0:
4
3 3
DRRD
0 2 3
0 0 0
3 1 0
4 5
DRRRRDD
0 1 0 2 3
0 0 0 0 0
-1 0 -3 -3 0
0 0 0 -1 0
2 3
RRD
0 0 0
0 1 0
5 5
DDDDRRRR
0 25 2 9 11
0 6 13 20 22
0 17 24 1 8
0 3 10 12 19
0 0 0 0 0

Example Output 0:
1 2 3
2 3 1
3 1 2
-6 1 0 2 3
7 -1 3 2 -11
-1 0 -3 -3 7
0 0 0 -1 1
0 -1 1
0 1 -1
18 25 2 9 11
4 6 13 20 22
15 17 24 1 8
21 3 10 12 19
7 14 16 23 5

Notes:
In the first test case, the grid has been filled such that every row and column contains the numbers $$$1, 2, 3$$$ in some order, resulting in a common sum of $$$6$$$.

In the second test case, the grid has been filled such that all rows and columns sum to $$$0$$$.

Example input:
4
3 3
DRRD
0 2 3
0 0 0
3 1 0
4 5
DRRRRDD
0 1 0 2 3
0 0 0 0 0
-1 0 -3 -3 0
0 0 0 -1 0
2 3
RRD
0 0 0
0 1 0
5 5
DDDDRRRR
0 25 2 9 11
0 6 13 20 22
0 17 24 1 8
0 3 10 12 19
0 0 0 0 0


Example output:
1 2 3
2 3 1
3 1 2
-6 1 0 2 3
7 -1 3 2 -11
-1 0 -3 -3 7
0 0 0 -1 1
0 -1 1
0 1 -1
18 25 2 9 11
4 6 13 20 22
15 17 24 1 8
21 3 10 12 19
7 14 16 23 5