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)

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

class PriorityQueue<T> where T : IComparable<T> {
    private List<T> _buf = new List<T>();
    private IComparer<T> _comp;

    private void Swap(int a, int b) {
        T t = _buf[a];
        _buf[a] = _buf[b];
        _buf[b] = t;
    }

    private int Compare(T a, T b) {
        if (_comp == null) return a.CompareTo(b);
        return _comp.Compare(a, b);
    }

    public int Count { get { return _buf.Count; } }

    public PriorityQueue() {
    }

    public PriorityQueue(IComparer<T> comp) {
        _comp = comp;
    }

    public T Peek() {
        if (Count == 0) throw new InvalidOperationException("Queue empty");
        return _buf[0];
    }

    public void Enqueue(T x) {
        _buf.Add(x);

        // shiftup
        int p = Count-1;
        while (p > 0) {
            int parent = (p - 1) / 2;
            if (Compare(_buf[parent], _buf[p]) <= 0)
                break;
            Swap(parent, p);
            p = parent;
        }
    }

    public T Dequeue() {
        if (Count == 0) throw new InvalidOperationException("Queue empty");

        T ret = _buf[0];
        _buf[0] = _buf[Count-1];
        _buf.RemoveAt(Count-1);

        // shiftdown
        int p = 0;
        while (p < Count) {
            int c = p * 2 + 1; // 左の子
            if (c >= Count) break;

            if (c+1 < Count) { // c+1 は右の子
                if (Compare(_buf[c+1], _buf[c]) < 0) { // 右の子のほうが小さい
                    c++;
                }
            }
            if (Compare(_buf[p], _buf[c]) <= 0)
                break;
            Swap(p, c);
            p = c;
        }
        return ret;
    }
}

struct D : IComparable<D> {
    public int node;
    public long cost;

    public int CompareTo(D o) {
        if (cost == o.cost) return 0;
        if (cost < o.cost) return -1;
        return 1;
    }
}

class Program {
    static int ReadInt() { return int.Parse(Console.ReadLine()); }
    static int[] ReadInts() { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
    static string[] ReadStrings() { return Console.ReadLine().Split(); }

    struct E {
        public int node;
        public int cost;
    }

    static long[] Calc(int k, int n, List<E>[] adj) {
        var used = new bool[n + 1];
        var cost = new long[n + 1];

        var q = new PriorityQueue<D>();
        q.Enqueue(new D { node = k, cost = 0 });
        while (q.Count > 0) {
            var d = q.Dequeue();
            if (used[d.node]) continue;
            used[d.node] = true;

            cost[d.node] = d.cost;

            foreach (var e in adj[d.node]) {
                q.Enqueue(new D { node = e.node, cost = d.cost + e.cost });
            }
        }

        return cost;
    }

    static void Main() {
        int n = ReadInt();

        var adj = new List<E>[n + 1];
        for (int i = 0; i < adj.Length; i++)
            adj[i] = new List<E>();
        for (int i = 0; i < n - 1; i++) {
            var abc = ReadInts();
            int a = abc[0], b = abc[1], c = abc[2];
            adj[a].Add(new E { node = b, cost = c });
            adj[b].Add(new E { node = a, cost = c });
        }

        var qk = ReadInts();
        int q = qk[0], k = qk[1];

        var cost = Calc(k, n, adj);
        for (int i = 0; i < q; i++) {
            var xy = ReadInts();
            int x = xy[0], y = xy[1];

            var ans = cost[x] + cost[y];
            Console.WriteLine(ans);

        }
    }
}