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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Text;

namespace AtTest.D_Challenge
{
    class ABC_070
    {
        static Node[] nodes;
        static long[] distances;
        static bool[] isMin;

        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            nodes = new Node[n];
            distances = new long[n];
            isMin = new bool[n];
            for (int i = 0; i < n; i++)
            {
                nodes[i] = new Node(n);
                distances[i] = -1;
                isMin[i] = false;
            }
            for (int i = 0; i < n-1; i++)
            {
                int[] abc = ReadInts();
                nodes[abc[0] - 1].edges.Add(new Edge(abc[1] - 1, abc[2]));
                nodes[abc[1] - 1].edges.Add(new Edge(abc[0] - 1, abc[2]));
            }
            int[] qk = ReadInts();
            distances[qk[1] - 1] = 0;
            isMin[qk[1] - 1] = true;
            Dijkstra(qk[1] - 1);

            var res = new long[qk[0]];
            for (int i = 0; i < qk[0]; i++)
            {
                int[] xy = ReadInts();
                res[i] = distances[xy[0] - 1]
                    + distances[xy[1] - 1];
            }
            for(int i = 0; i < qk[0]; i++)
            {
                Console.WriteLine(res[i]);
            }
        }

        //最大距離を帰す
        static void Dijkstra(int start)
        {
            Node startNode = nodes[start];
            int cnt = 1;
            int nowIndex = start;

            while (cnt < nodes.Length)
            {
                for (int i = 0; i < nodes[nowIndex].edges.Count; i++)
                {
                    int destIndex = nodes[nowIndex].edges[i].toIndex;
                    if (isMin[destIndex]) continue;//確定ノードは無視

                    long distance = distances[nowIndex]
                        + nodes[nowIndex].edges[i].distance;
                    if (distance < distances[destIndex]
                        || distances[destIndex] == -1)
                    {
                        distances[destIndex] = distance;
                    }
                }

                int settleIndex = -1;
                for (int i = 0; i < distances.Length; i++)
                {
                    if (isMin[i] || distances[i] == -1) continue;

                    if (settleIndex == -1
                        || distances[i] < distances[settleIndex])
                    {
                        settleIndex = i;
                    }
                }
                if (settleIndex == -1) break;
                isMin[settleIndex] = true;
                nowIndex = settleIndex;
                cnt++;
            }
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        class Node
        {
            public List<Edge> edges;
            public Node(int length)
            {
                distances = new long[length];
                isMin = new bool[length];
                for (int i = 0; i < length; i++)
                {
                    distances[i] = -1;
                }
                edges = new List<Edge>();
            }
        }

        class Edge
        {
            public int toIndex;
            public int distance;

            public Edge(int toIndex, int distance)
            {
                this.toIndex = toIndex;
                this.distance = distance;
            }
        }
    }
}