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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

//探索
fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val branches = Array(n + 1) { mutableListOf<Pair<Int, Long>>() }
    (1 until n).forEach {
        val (a, b, c) = readLine()!!.split(' ').map(String::toLong)
        branches[a.toInt()].add(Pair(b.toInt(), c))
        branches[b.toInt()].add(Pair(a.toInt(), c))
    }
    val minCost = LongArray(n+1) { Long.MAX_VALUE / 3 }
    val (q, k) = readLine()!!.split(' ').map(String::toLong)

    var queue = ArrayDeque<Int>().apply { this.add(k.toInt()) }
    minCost[k.toInt()] = 0
    while (queue.isNotEmpty()) {
        val cur = queue.pollFirst()!!
        val curCost = minCost[cur]
        val bs = branches[cur]
        for (b in bs) {
            val (to, cost) = b
            if (minCost[to] > curCost + cost) {
                minCost[to] = curCost + cost
                queue.add(to)
            }
        }
    }
    (1..q).forEach {
        val (from, to) = readLine()!!.split(' ').map(String::toInt)
        println(minCost[from] + minCost[to])
    }
}