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. 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 $