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.util.*;
public class Main {
		
	static List<ArrayList<int[]>> to;
	static int x, y;
	static long memo[];
	
	public static void main(String[] args) {
		
		//入力値の受け取り
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		
		//連結リスト
		to = new ArrayList();
		for(int i=0;i<N;i++) {
			to.add(new ArrayList<int[]>());
		}
		
		for(int i=0;i<N-1;i++) {
			int a = sc.nextInt(), b = sc.nextInt(), c = sc.nextInt();
			a--;b--;
			int t[] = {b,c};
			to.get(a).add(t);
			int u[] = {a,c};
			to.get(b).add(u);
		}
		int Q = sc.nextInt(), K = sc.nextInt();
		K--;
		
		//問題
		int q[][] = new int[Q][2];
		for(int i=0;i<Q;i++) {
			int x = sc.nextInt(), y = sc.nextInt();
			x--;y--;
			q[i][0]=x; q[i][1]=y;
		}
		sc.close();
		
		memo = new long[N];//Kからの距離をメモする配列
		memo[K]=0;
		dfs(K, -1, 0L);
		StringBuilder sb = new StringBuilder();
		for(int i=0;i<Q;i++) {
			int x = q[i][0];  int y = q[i][1];
			long ans = memo[x]+memo[y];
			sb.append(ans+"\n");
		}	
		System.out.println(sb.toString());
	}
	
	static void dfs(int a, int p, long len) {
		for(int t[] : to.get(a)) {
			int na = t[0];
			int d = t[1];
			if(na == p)continue;
			memo[na]=len+d;
			dfs(na , a, len+d);
		}
	}
	
}