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## 문제

Peanut is going for a holiday to the city Silvermill, and therefore he needs a map of Silvermill. Unfortunately, his computer is broken, and so he cannot Google for the map.

Silvermill is a city consisting of N road junctions, numbered 1 to N, and N − 1 roads, with each road i connecting two road junctions Ai and Bi in both directions. This road also takes Wi minutes to traverse in either direction. It is guranteed that the city is fully connected, meaning it is possible to travel from any road junction to any other road junction using the roads in the city. To avoid congestion, the governor of Silvermill has decided that there will be no more than three roads connected to each junction in the city.

Peanut needs to obtain a map of Silvermill. In other words, he needs to obtain (Ai, Bi, Wi) for i = 1, . . . , N − 1.

Peanut has hired a cartographer in Silvermill to accomplish this task. As the cartographer is not very skilled, he can only answer a very simple question: what is the minimum amount of time, in minutes, required to travel between road junctions X and Y ? Peanut did not pay enough money to this cartographer, so he only answers Q such questions before he quits his job.

Peanut needs you to help him to design a list of questions so that he can map out Silvermill and enjoy his holiday. Can you help him?

## 구현

In this task, you are asked to implement the following function: (It is different from the normal task, which requires the program to read from standard input and output to standard output.)

void find_roads(int N, int Q, int A[], int B[], int W[])

This function will be called exactly once with two input parameters and three output parameters. The two input parameters are N and Q. N is the number of road junctions while Q is the maximum number of queries allowed. The three output parameters are A, B and W. You are required to determine the N − 1 roads in the city and return them in the arrays A, B and W. The endpoints of the roads and the roads themselves can be in any order.

You are allowed to call the following grader function to complete the task:

long long get_distance(int X, int Y)

This function will return a single integer, the time taken to travel between road junctions X and Y , in minutes. If you call this function more than Q times or provide invalid road junction numbers as arguments, the program will terminate immediately and you will be given a Wrong Answer verdict.

Consider the city map found in Figure 4. Suppose Q = 500000. Then, you are asked to implement the function:

find_roads(5, 500000, A[], B[], W[])

A possible interaction between your program find roads and the grader functions get distance could be as follows:

• get_distance(5, 4) = 10
The get_distance function is asked to find the distance between road junctions 4 and 5. The answer is 10, as it takes 3 minutes to get from road junction 5 to 3, then another 7 minutes to get from road junction 3 to 4.
• get_distance(2, 4) = 1
The get_distance function is asked to find the distance between road junctions 2 and 4. The answer is 1, as it takes 1 minute to directly travel from road junction 2 to 4.
• get_distance(1, 3) = 15
The get_distance function is asked to find the distance between road junctions 1 and 3. The answer is 15, as it takes 8 minutes to get from road junction 1 to 4, then another 7 minutes to get from road junction 4 to 3.
• get_distance(1, 2) = 9
The get_distance function is asked to find the distance between road junctions 1 and 2. The answer is 9, as it takes 8 minutes to get from road junction 1 to 4, then another 1 minutes to get from road junction 4 to 2.

At this point, the contestant’s find_roads function decides it has enough information to deduce the map of the city. It sets A = [3, 4, 4, 5], B = [4, 1, 2, 3] and W = [7, 8, 1, 3] and then terminates. This is a possible correct answer. The endpoints of the roads and the roads themselves can be provided in any order.

## 제한

• 2 ≤ N ≤ 1000,
• 1 ≤ Ai, Bi ≤ N,
• 1 ≤ Wi ≤ 109.

• Q = 500000
• Wi = 1

• Q = 500000

## 서브태스크 3 (13점)

• Q = 12000
• Each junction has at most two roads connected to it, Wi = 1

## 서브태스크 4 (19점)

• Q = 12000
• Each junction has at most two roads connected to it

• Q = 25000