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: Accepted)

//
// ABC070D
// URL : https://atcoder.jp/contests/abc070/tasks/abc070_d
// 
using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;

namespace AtCoder
{
    class ABC070D
    {
        class TreeEdge
        {
            public long idx;
            public long cost;
            public TreeEdge() {
                idx = 0;
                cost = 0;
            }
            public TreeEdge(long _idx,long _cost)
            {
                idx = _idx;
                cost = _cost;
            }
        }
        class Query
        {
            public long start;
            public long end;
            public Query() { start = end = 0; }
            public Query(long s, long e)
            {
                start = s;
                end = e;
            }
        }
        static List<Query> qList = null;


        static long N = 0;
        static long Q = 0;
        static long K = 0;

        static long[] DistanceFromPointK = null;
        static List<List<TreeEdge>> TreeNode = null;//TreeNode[A] : 木の節Aの辺情報を格納

        static void Main(string[] args)
        {
            preprocess();
            // 頂点数
            N = long.Parse(Console.ReadLine());
            DistanceFromPointK = new long[(int)N];
            TreeNode = new List<List<TreeEdge>>((int)N);//頂点数分確保
            for (int i = 0; i < N; ++i)
            {
                DistanceFromPointK[i] = long.MaxValue;
                TreeNode.Add(new List<TreeEdge>());
            }
            for (int i = 0; i < N-1; ++i){//edgeの数だけ
                long[] inputLongArray = Console.ReadLine().Split(' ').Select(_inputStr => long.Parse(_inputStr)).ToArray();
                long pA = inputLongArray[0];
                long pB = inputLongArray[1];
                long dist = inputLongArray[2];
                //配列のindexにするため0基準に
                pA--;
                pB--;
                //index A番目に、点Aから点Bへの辺情報を代入
                TreeNode[(int)pA].Add(new TreeEdge(pB, dist));
                //index B番目に、点Bから点Aへの辺情報を代入
                TreeNode[(int)pB].Add(new TreeEdge(pA, dist));
            }
            {
                long[] inputLongArray = Console.ReadLine().Split(' ').Select(_inputStr => long.Parse(_inputStr)).ToArray();
                Q = inputLongArray[0];
                K = inputLongArray[1]-1;//頂点indexなので1引く
            }
            qList = new List<Query>((int)Q);
            for (int i = 0; i < Q; ++i)
            {
                long[] inputLongArray = Console.ReadLine().Split(' ').Select(_inputStr => long.Parse(_inputStr)).ToArray();
                qList.Add(new Query(inputLongArray[0]-1, inputLongArray[1]-1) );//頂点indexなので1引く
            }

            //事前計算
            DFS(K, -1, 0);

            var ans = new List<long>((int)Q);
            for(int i = 0; i < Q; ++i)
            {
                long startIdx = qList[i].start;
                long endIdx = qList[i].end;
                long Cost_startToK = DistanceFromPointK[startIdx];
                long Cost_KToEnd = DistanceFromPointK[endIdx];
                ans.Add(Cost_startToK + Cost_KToEnd);
            }

            foreach (var l in ans)
            {
                Console.WriteLine(l.ToString());
            }
            Console.Out.Flush();
        }


        //深さ優先探索
        //今の点、親の点
        public static void DFS(long currentVertex,long parentVertex, long cost)
        {
            //KからcurrentVertexまでの距離を保存
            DistanceFromPointK[currentVertex] = cost;

            //次に見る点を探す
            foreach(var edge in TreeNode[(int)currentVertex])
            {
                //次に見る点が親だったら探索しなくてもいい
                if(edge.idx == parentVertex) { continue; }
                DFS(edge.idx, currentVertex, cost + edge.cost);
            }
        }


        //---------------------------------------------------------------------------------
        /// <summary>
        /// 
        /// </summary>
        public static void preprocess()
        {
            //出力高速化
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
        }


        /// <summary>
        /// 与えられた数が素数かどうかを計算する
        /// </summary>
        /// <param name="num">対象数</param>
        /// <returns>true:素数, false:素数ではない(合成数)</returns>
        public static bool isPrime(int num)
        {
            if (num < 2) return false;
            else if (num == 2) return true;
            else if (num % 2 == 0) return false;

            double sqrtNum = Math.Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0)
                {
                    return false;
                }
            }
            return true;
        }

        /// <summary>
        /// 順列mPnを計算する
        /// </summary>
        /// <param name="m"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public static long Permutation(long m, long n)
        {
            long ret = 1;
            for(var i = 0; i < n; ++i)
            {
                ret *= m - i;
            }
            return ret;
        }
        /// <summary>
        /// 組み合わせmCnを計算する
        /// </summary>
        /// <param name="m"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public static long Combination(long m, long n)
        {
            if(m == n || n == 0)
            {
                return 1;
            }
            long ans = 1;
            for(var i = 0; i <= n; ++i)
            {
                ans *= (m - i + 1) / i;
            }
            return ans;
        }
    }
}