Safety in Treeland SOLUTIONS SAFETR
The realm of Treeland comprises of N urban areas (numbered 1 through N) associated by N−1 bidirectional streets so that there is a way between each pair of urban areas.
So as to expand security in Treeland, the administration chose to set up police workplaces in K of its urban areas. For each substantial I, the I-th office is in city Vi and it has a range of proficiency Ri.
We should characterize the security level Si of every city I as follows:
At first, the security level of every city is equivalent to zero.
At that point, for each police office j that was fabricated (1≤j≤K), the security levels change in the accompanying way:
The security level of the city Vj increments by Rj.
The security levels of all urban communities at the separation 1 from Vj increment by Rj−1.
The security levels of all urban areas at the separation Rj−1 from Vj increment by 1.
Officially, for every city I, the j-th office expands the security level of this city by max(0,Rj−distance(i,Vj)).
Alice was responsible for ascertaining the new security levels of all urban communities after the workplaces were assembled. She previously completed her activity and saw an intriguing incident: for each substantial I, SVi=Ri holds. Presently she has provoked you to discover the security levels everything being equal.
The primary line of the information contains a solitary whole number T signifying the quantity of experiments. The portrayal of T experiments follows.
The primary line of each experiment contains two space-isolated whole numbers N and K.
At that point, N−1 lines follow. Every one of these lines contains two space-isolated whole numbers u and v signifying that urban communities u and v are associated by a street.
K more lines follow. For each substantial I, the I-th of these lines contains two space-isolated whole numbers Vi and Ri.
For each experiment, print a solitary line containing N space-isolated numbers S1,S2,… ,SN.
1≤Vi≤N for each legitimate I
V1,V2,… ,VK are pairwise particular
1≤Ri for each legitimate I
the whole of N over all experiments doesn’t surpass 8⋅105
0 1 0 1
0 2 0 2
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