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# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var N = int.Parse(Console.ReadLine());
            var graph = new List<Tuple<int, long>>[N].Select(x => new List<Tuple<int, long>>()).ToArray();
            for (var i = 0; i < N - 1; i++)
            {
                var abc = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
                var a = abc[0] - 1;
                var b = abc[1] - 1;
                long c = abc[2];
                graph[a].Add(new Tuple<int, long>(b, c));
                graph[b].Add(new Tuple<int, long>(a, c));
            }

            var QK = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var Q = QK[0];
            var K = QK[1];

            var xk = new long[N - 1];
            var ky = new long[N - 1];

            for (var i = 0; i < N - 1; i++)
            {
                var queue = new Queue<int>();
                queue.Enqueue(i);
                var depths = Enumerable.Repeat(-1, N).ToArray();
                depths[i] = 0;
                var costs = Enumerable.Repeat((long)1e18 + 1, N).ToArray();
                costs[i] = 0;
                while (queue.Any())
                {
                    var current = queue.Dequeue();
                    foreach (var next in graph[current])
                    {
                        if (costs[next.Item1] <= costs[current] + next.Item2) continue;
                        depths[next.Item1] = depths[current] + 1;
                        costs[next.Item1] = costs[current] + next.Item2;
                        queue.Enqueue(next.Item1);
                    }
                }
                xk[i] = costs[K - 1];
                if (i == K - 1) ky = costs;
            }

            var query = new Tuple<int, int>[Q];
            for (var i = 0; i < Q; i++)
            {
                var xy = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
                query[i] = new Tuple<int, int>(xy[0] - 1, xy[1] - 1);
            }

            for (var i = 0; i < Q; i++)
            {
                Console.WriteLine(xk[query[i].Item1] + ky[query[i].Item2]);
            }
        }
    }
}