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: Accepted)


import java.io.*;
import java.util.*;
public class Main{
	public static void main(String[] args)throws Throwable {
		MyScanner sc=new MyScanner();
		PrintWriter pw=new PrintWriter(System.out);
		
		n=sc.nextInt();
		adj=new ArrayList [n];
		for(int i=0;i<n;i++)
			adj[i]=new ArrayList<Integer>();
		int [] x=new int [n-1];
		int [] y=new int [n-1];
		int [] z=new int [n-1];
		for(int i=0;i<n-1;i++){
			x[i]=sc.nextInt()-1;
			y[i]=sc.nextInt()-1;
			z[i]=sc.nextInt();
			adj[x[i]].add(y[i]);
			adj[y[i]].add(x[i]);
		}
		preProcessing();
		for(int i=0;i<n-1;i++)
			if(level[x[i]]>level[y[i]])
				cost[x[i]]=z[i];
			else
				cost[y[i]]=z[i];
		dfs2(0);
		int q=sc.nextInt();
		k=sc.nextInt()-1;
		while(q-->0){
			int u=sc.nextInt()-1;
			int v=sc.nextInt()-1;
			pw.println(min_dis(u, v));
		}
		
		pw.flush();
		pw.close();
	}
	
	static long min_dis(int u,int v){
		int l=query(u, v);
		int uk=query(u, k);
		int vk=query(v, k);
		int lk=query(l, k);
		if(lk==l && (uk==k || vk==k))
			return path_len(u, v, l);
		else
			return path_len(u, k, uk)+path_len(v, k, vk);
	}
	
	static long path_len(int u,int v,int l){
		return cost[u]+cost[v]-2*cost[l];
	}
	
	static int n,k;
	static int [][] ansector;
	static int [] parent,level;
	static long [] cost;
	static ArrayList<Integer> [] adj;
	
	static void preProcessing(){
		parent=new int [n];
		level=new int [n];
		cost=new long [n];
		parent[0]=-1;
		dfs(0, 0);
		int log=(int)Math.ceil(Math.log(n)/Math.log(2));
		ansector=new int [n][log];
		for(int [] x : ansector)
			Arrays.fill(x, -1);
		for(int i=0;i<n;i++)
			ansector[i][0]=parent[i];				
		for(int j=1;(1<<j)<n;j++)
			for(int i=0;i<n;i++)
				if(ansector[i][j-1]!=-1)
					ansector[i][j]=ansector[ansector[i][j-1]][j-1];
	}
	
	public static void dfs(int u,int h){
		level[u]=h;
		for(int v : adj[u])
			if(v!=parent[u]){
				parent[v]=u;
				dfs(v, h+1);
			}
	}
	
	static void dfs2(int u){
		for(int v : adj[u])
			if(v!=parent[u]){
				cost[v]+=cost[u];
				dfs2(v);
			}
	}
	
	public static int query(int u,int v){
		if(level[u]<level[v]){
			int tmp=u;
			u=v;
			v=tmp;
		}
		int log=1;
		for(log=1;(1<<log)<=level[u];log++);
		log--;
		
		for(int i=log;i>=0;i--)
			if(level[u]-(1<<i)>=level[v])
				u=ansector[u][i];
		
		if(u==v)
			return u;
		
		for(int i=log;i>=0;i--)
			if(ansector[u][i]!=-1 && ansector[u][i]!=ansector[v][i]){
				u=ansector[u][i];
				v=ansector[v][i];
			}
		return parent[u];
	}
	
	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {while (st == null || !st.hasMoreElements()) {
			try {st = new StringTokenizer(br.readLine());}
			catch (IOException e) {e.printStackTrace();}}
		return st.nextToken();}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() {return Double.parseDouble(next());}
		String nextLine(){String str = "";
		try {str = br.readLine();}
		catch (IOException e) {e.printStackTrace();}
		return str;}
	}
}