Problem:
Score : 400 points

Problem Statement

You are given a tree with N vertices.

Here, a tree is a kind of graph, and more specifically, a connected undirected graph with N-1 edges, where N is the number of its vertices.

The i-th edge (1≤i≤N-1) connects Vertices a_i and b_i, and has a length of c_i.

You are also given Q queries and an integer K. In the j-th query (1≤j≤Q):

find the length of the shortest path from Vertex x_j and Vertex y_j via Vertex K.

Constraints

3≤N≤10^5

1≤a_i,b_i≤N (1≤i≤N-1)

1≤c_i≤10^9 (1≤i≤N-1)

The given graph is a tree.

1≤Q≤10^5

1≤K≤N

1≤x_j,y_j≤N (1≤j≤Q)

x_j≠y_j (1≤j≤Q)

x_j≠K,y_j≠K (1≤j≤Q)

Input

Input is given from Standard Input in the following format:

N
a_1 b_1 c_1
:
a_{N-1} b_{N-1} c_{N-1}
Q K
x_1 y_1
:
x_{Q} y_{Q}

Output

Print the responses to the queries in Q lines.

In the j-th line j(1≤j≤Q), print the response to the j-th query.

Sample Input 1

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

Sample Output 1

3
2
4

The shortest paths for the three queries are as follows:

Query 1: Vertex 2 → Vertex 1 → Vertex 2 → Vertex 4 : Length 1+1+1=3

Query 2: Vertex 2 → Vertex 1 → Vertex 3 : Length 1+1=2

Query 3: Vertex 4 → Vertex 2 → Vertex 1 → Vertex 3 → Vertex 5 : Length 1+1+1+1=4

Sample Input 2

7
1 2 1
1 3 3
1 4 5
1 5 7
1 6 9
1 7 11
3 2
1 3
4 5
6 7

Sample Output 2

5
14
22

The path for each query must pass Vertex K=2.

Sample Input 3

10
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
6 7 1000000000
7 8 1000000000
8 9 1000000000
9 10 1000000000
1 1
9 10

Sample Output 3

17000000000

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

// ABC 70-D
// https://beta.atcoder.jp/contests/abc070/tasks/abc070_d

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);

		int N = in.nextInt();
		long[][] map = new long[N][N];
		
		for (int i = 0; i < N - 1; i++) {
			int a = in.nextInt() - 1;
			int b = in.nextInt() - 1;
			int c = in.nextInt();
			
			map[a][b] = c;
			map[b][a] = c;
		}
		int Q = in.nextInt();
		int K = in.nextInt() - 1;
		
		long[] toK = new long[N];
		
		for (int i = 0; i < N; i++) {
			if (i != K) {
				PriorityQueue pq = new PriorityQueue<State>();
				int[] visited = new int[N];
				pq.add(new State(i, 0));
				boolean shouldContinue = true;
				while (shouldContinue && pq.size() > 0) {
					State s = (State) pq.poll();
					visited[s.curr] = 1;
					if (s.curr == K) {
						toK[i] = s.dist;
						shouldContinue = false;
					} else {
						for (int j = 0; j < N; j++) {
							if (map[s.curr][j] != 0 && visited[j] == 0) {
								pq.add(new State(j, s.dist + map[s.curr][j]));
							}
						}
					}
				}
			}			
		}
		
		long[] fromK = new long[N];
		
		for (int i = 0; i < N; i++) {
			if (i != K) {
				PriorityQueue pq = new PriorityQueue<State>();
				pq.add(new State(i, 0));
				int[] visited = new int[N];
				boolean shouldContinue = true;
				while (shouldContinue && pq.size() > 0) {
					State s = (State) pq.poll();
					visited[s.curr] = 1;
					if (s.curr == K) {
						fromK[i] = s.dist;
						shouldContinue = false;
					} else {
						for (int j = 0; j < N; j++) {
							if (map[s.curr][j] > 0 && visited[j] == 0) {
								pq.add(new State(j, s.dist + map[s.curr][j]));
							}
						}
					}
				}
			}
		}
		
		for (int i = 0; i < Q; i++) {
			int start = in.nextInt() - 1;
			int end = in.nextInt() - 1;
			System.out.println(toK[start] + fromK[end]);
		}
	}
	
	public static void print(String name, int[] arr) {
		System.out.println(name);
		for (int i = 0; i < arr.length; i++) {
			System.out.printf("%d ", arr[i]);
		}
		System.out.println();
	}
	
}

class State implements Comparable<State> {
	int curr;
	long dist;
	
	public State(int curr, long dist) {
		this.curr = curr;
		this.dist = dist;
	}

	@Override
	public int compareTo(State o) {
		if (this.dist - o.dist < 0) {
			return -1;
		} else if (this.dist - o.dist > 0) {
			return 1;
		} else {
			return 0;
		}
	}
	
	
}