Lena and Matrix

题意翻译

$t$ 组数据，每组给定一个由字符 `W` 或 `B` 组成的 $n\times m$ 的矩阵。求这样一个点的坐标，满足其到图中任何一个 `B` 的最大曼哈顿距离最小。 若有多解，可任意输出一个。 $1\le t\le 10000,2\le n,m\le 1000,\sum nm\le 10^6$

题目描述

Lena is a beautiful girl who likes logical puzzles. As a gift for her birthday, Lena got a matrix puzzle! The matrix consists of $ n $ rows and $ m $ columns, and each cell is either black or white. The coordinates $ (i,j) $ denote the cell which belongs to the $ i $ -th row and $ j $ -th column for every $ 1\leq i \leq n $ and $ 1\leq j \leq m $ . To solve the puzzle, Lena has to choose a cell that minimizes the Manhattan distance to the farthest black cell from the chosen cell. More formally, let there be $ k \ge 1 $ black cells in the matrix with coordinates $ (x_i,y_i) $ for every $ 1\leq i \leq k $ . Lena should choose a cell $ (a,b) $ that minimizes $$\max_{i=1}^{k}(|a-x_i|+|b-y_i|). $$ As Lena has no skill, she asked you for help. Will you tell her the optimal cell to choose?

输入输出格式

输入格式

There are several test cases in the input data. The first line contains a single integer $ t $ ( $ 1\leq t\leq 10\,000 $ ) — the number of test cases. This is followed by the test cases description. The first line of each test case contains two integers $ n $ and $ m $ ( $ 2\leq n,m \leq 1000 $ ) — the dimensions of the matrix. The following $ n $ lines contain $ m $ characters each, each character is either 'W' or 'B'. The $ j $ -th character in the $ i $ -th of these lines is 'W' if the cell $ (i,j) $ is white, and 'B' if the cell $ (i,j) $ is black. It is guaranteed that at least one black cell exists. It is guaranteed that the sum of $ n\cdot m $ does not exceed $ 10^6 $ .

输出格式

For each test case, output the optimal cell $ (a,b) $ to choose. If multiple answers exist, output any.

输入输出样例

输入样例 #1

5
3 2
BW
WW
WB
3 3
WWB
WBW
BWW
2 3
BBB
BBB
5 5
BWBWB
WBWBW
BWBWB
WBWBW
BWBWB
9 9
WWWWWWWWW
WWWWWWWWW
BWWWWWWWW
WWWWWWWWW
WWWWBWWWW
WWWWWWWWW
WWWWWWWWW
WWWWWWWWW
WWWWWWWWB

输出样例 #1

2 1
2 2
1 2
3 3
6 5

说明

In the first test case the two black cells have coordinates $ (1,1) $ and $ (3,2) $ . The four optimal cells are $ (1,2) $ , $ (2,1) $ , $ (2,2) $ and $ (3,1) $ . It can be shown that no other cell minimizes the maximum Manhattan distance to every black cell. In the second test case it is optimal to choose the black cell $ (2,2) $ with maximum Manhattan distance being $ 2 $ .