Air Conditioners

题意翻译

有 $ q $ 组数据，每组第一排表示有 $ n $ 个方格和 $ k $ 个空调，第二排是每个空调的位置 $ a_i $ ,第三排是每个空调的温度 $ t_i $ 。 每个空调对周围的影响是递减的，所以一个空调周围的温度是公差为 $ 1 $ 的递增等差数列。如果一个方格同时被多个空调影响，那么取最小值。空调所在的方格温度就是空调的温度。 输出所有方格的温度。 $ 1 \le q \le 10^4 , 1 \le n \le 3 \cdot 10^5 , 1 \le k \le n , 1 \le a_i \le n , 1 \le t_i \le 10^9 $ , 保证所有 $ n $ 的总和不超过 $ 3 \cdot 10^5 $ 。

题目描述

On a strip of land of length $ n $ there are $ k $ air conditioners: the $ i $ -th air conditioner is placed in cell $ a_i $ ( $ 1 \le a_i \le n $ ). Two or more air conditioners cannot be placed in the same cell (i.e. all $ a_i $ are distinct). Each air conditioner is characterized by one parameter: temperature. The $ i $ -th air conditioner is set to the temperature $ t_i $ . Example of strip of length $ n=6 $ , where $ k=2 $ , $ a=[2,5] $ and $ t=[14,16] $ .For each cell $ i $ ( $ 1 \le i \le n $ ) find it's temperature, that can be calculated by the formula $ $\min_{1 \le j \le k}(t_j + |a_j - i|), $ $ </p><p>where $ |a\_j - i| $ denotes absolute value of the difference $ a\_j - i $ .</p><p>In other words, the temperature in cell $ i $ is equal to the minimum among the temperatures of air conditioners, increased by the distance from it to the cell $ i $ .</p><p>Let's look at an example. Consider that $ n=6, k=2 $ , the first air conditioner is placed in cell $ a\_1=2 $ and is set to the temperature $ t\_1=14 $ and the second air conditioner is placed in cell $ a\_2=5 $ and is set to the temperature $ t\_2=16 $ . In that case temperatures in cells are:</p><ol> <li> temperature in cell $ 1 $ is: $ \\min(14 + |2 - 1|, 16 + |5 - 1|)=\\min(14 + 1, 16 + 4)=\\min(15, 20)=15 $ ; </li><li> temperature in cell $ 2 $ is: $ \\min(14 + |2 - 2|, 16 + |5 - 2|)=\\min(14 + 0, 16 + 3)=\\min(14, 19)=14 $ ; </li><li> temperature in cell $ 3 $ is: $ \\min(14 + |2 - 3|, 16 + |5 - 3|)=\\min(14 + 1, 16 + 2)=\\min(15, 18)=15 $ ; </li><li> temperature in cell $ 4 $ is: $ \\min(14 + |2 - 4|, 16 + |5 - 4|)=\\min(14 + 2, 16 + 1)=\\min(16, 17)=16 $ ; </li><li> temperature in cell $ 5 $ is: $ \\min(14 + |2 - 5|, 16 + |5 - 5|)=\\min(14 + 3, 16 + 0)=\\min(17, 16)=16 $ ; </li><li> temperature in cell $ 6 $ is: $ \\min(14 + |2 - 6|, 16 + |5 - 6|)=\\min(14 + 4, 16 + 1)=\\min(18, 17)=17 $ . </li></ol><p>For each cell from $ 1 $ to $ n$ find the temperature in it.

输入输出格式

输入格式

The first line contains one integer $ q $ ( $ 1 \le q \le 10^4 $ ) — the number of test cases in the input. Then test cases follow. Before each test case, there is an empty line. Each test case contains three lines. The first line contains two integers $ n $ ( $ 1 \le n \le 3 \cdot 10^5 $ ) and $ k $ ( $ 1 \le k \le n $ ) — the length of the strip of land and the number of air conditioners respectively. The second line contains $ k $ integers $ a_1, a_2, \ldots, a_k $ ( $ 1 \le a_i \le n $ ) — positions of air conditioners on the strip of land. The third line contains $ k $ integers $ t_1, t_2, \ldots, t_k $ ( $ 1 \le t_i \le 10^9 $ ) — temperatures of air conditioners. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 3 \cdot 10^5 $ .

输出格式

For each test case output $ n $ integers separated by space: temperatures of air in cells.

输入输出样例

输入样例 #1

5

6 2
2 5
14 16

10 1
7
30

5 5
3 1 4 2 5
3 1 4 2 5

7 1
1
1000000000

6 3
6 1 3
5 5 5

输出样例 #1

15 14 15 16 16 17 
36 35 34 33 32 31 30 31 32 33 
1 2 3 4 5 
1000000000 1000000001 1000000002 1000000003 1000000004 1000000005 1000000006 
5 6 5 6 6 5