segment of place where there is length n there are k climate control systems: the I-th climate control system is set in cell artificial intelligence (1≤ai≤n). At least two climate control systems can't be put in a similar cell (for example all man-made intelligence are particular). Each climate control
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segment of place where there is length n there are k climate control systems: the I-th climate control system is set in cell
Each climate control system is characterized by one boundary: temperature. The I-th climate control system is set to the temperature ti.
Illustration of portion of length n=6, where k=2, a=[2,5] and t=[14,16].
For every cell I (1≤i≤n) discover it's temperature, that can be determined by the equation
min1≤j≤k(tj+|aj−i|),
where |aj−i| means outright worth of the distinction aj−i.
As such, the temperature in cell I is equivalent to the base among the temperatures of forced air systems, expanded by the separation from it to the cell I.
How about we take a gander at a model. Consider that n=6,k=2, the main forced air system is put in cell a1=2 and is set to the temperature t1=14 and the second forced air system is put in cell a2=5 and is set to the temperature t2=16.
Input :The primary line contains one integer q (1≤q≤104) — the number of experiments in the input. Then, at that point, experiments follow. Before each experiment, there is an unfilled line.
Each experiment contains three lines. The primary line contains two integers n (1≤n≤3⋅105) and k (1≤k≤n) — the length of the portion of land and the number of forced air systems individually. The subsequent line contains k integers a1,a2,… ,ak (1≤ai≤n) — places of climate control systems on the piece of land. The third line contains k integers t1,t2,… ,tk (1≤ti≤109) — temperatures of forced air systems. It is ensured that the amount of n over all experiments doesn't surpass 3⋅105.
Output :For each experiment output n integers isolated by space: temperatures of air in cells.
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