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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.util.*;

public class Main {

	public static void main(String[] args) {
		Main main = new Main();
		main.run();
	}

	class Edge{
		int to;
		int cost;
		Edge(int to, int cost){
			this.to=to;
			this.cost=cost;
		}
	}

	class P implements Comparable<P>{
		int v;
		long dist;
		P(int v, long dist){
			this.v=v;
			this.dist=dist;
		}
		@Override
		public int compareTo(P arg0) {
			return Long.compare(this.dist, arg0.dist);
		}
	}

	long d[];
	long INF = 1001001001001001L;
	ArrayList<ArrayList<Edge>> g = new ArrayList<>();
	public void run() {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		d = new long[n];
		for(int i=0; i<n; i++) {
			g.add(new ArrayList<>());
		}
		for(int i=0; i<n-1; i++) {
			int a=sc.nextInt();
			int b=sc.nextInt();
			a--;b--;
			int c=sc.nextInt();
			g.get(a).add(new Edge(b,c));
			g.get(b).add(new Edge(a,c));
		}

		int q=sc.nextInt();
		int k=sc.nextInt();
		k--;

		PriorityQueue<P> pq = new PriorityQueue<>();
		for(int i=0; i<n; i++) {
			d[i]=INF;
		}
		d[k]=0;
		pq.add(new P(k,0));
		while(!pq.isEmpty()) {
			P p = pq.poll();
			if(d[p.v]<p.dist) continue;
			for(Edge e : g.get(p.v)) {
				if(d[e.to] > d[p.v] + e.cost) {
					d[e.to] = d[p.v] + e.cost;
					pq.add(new P(e.to, d[e.to]));
				}
			}
		}
		for(int i=0; i<q; i++) {
			int x=sc.nextInt();
			int y=sc.nextInt();
			x--; y--;
			System.out.println(d[x]+d[y]);
		}
		sc.close();
	}





}