CF1985D Manhattan Circle

Given a $ n $ by $ m $ grid consisting of '.' and '#' characters, there exists a whole manhattan circle on the grid. The top left corner of the grid has coordinates $ (1,1) $ , and the bottom right corner has coordinates $ (n, m) $ . Point ( $ a, b $ ) belongs to the manhattan circle centered at ( $ h, k $ ) if $ |h - a| + |k - b| < r $ , where $ r $ is a positive constant. On the grid, the set of points that are part of the manhattan circle is marked as '#'. Find the coordinates of the center of the circle.

The first line contains $ t $ ( $ 1 \leq t \leq 1000 $ ) — the number of test cases. The first line of each test case contains $ n $ and $ m $ ( $ 1 \leq n \cdot m \leq 2 \cdot 10^5 $ ) — the height and width of the grid, respectively. The next $ n $ lines contains $ m $ characters '.' or '#'. If the character is '#', then the point is part of the manhattan circle. It is guaranteed the sum of $ n \cdot m $ over all test cases does not exceed $ 2 \cdot 10^5 $ , and there is a whole manhattan circle on the grid.

For each test case, output the two integers, the coordinates of the center of the circle.