Safety in Treeland SOLUTIONS SAFETR

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. 

 

Information 

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. 

 

Yield 

For each experiment, print a solitary line containing N space-isolated numbers S1,S2,… ,SN. 

 

Requirements 

1≤T≤2,000 

2≤N,K≤8⋅105 

1≤u,v≤N 

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 

 

Model Input 

5 2 

5 2 

5 4 

5 3 

3 1 

2 1 

5 1 

5 2 

5 2 

1 2 

2 4 

3 1 

4 2 

5 2 

 

Model Output 

0 1 0 1 

0 2 0 2

 

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