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)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val g = Graph(n,n-1)
    val (q,k) = readLine()!!.split(" ").map { it.toInt() }
    val qs = (1..q).map { readLine()!!.split(" ").map { it.toInt() } }

    val d = g.makeRootedTree(k)
    qs.map {
        d[it[0]] + d[it[1]]
    }.joinToString("\n").let { println(it) }
}

class Graph (val N: Int, val M: Int){

    data class Edge(val to: Int, val cost: Long)

    val adj = run {
        val adjList = Array<MutableList<Edge>>(N+1){ mutableListOf()}
        (1..M).forEach {
            val line = readLine()!!.split(" ")
            val from = line[0].toInt()
            val to = line[1].toInt()
            val cost = line.getOrElse(2){"1"}.toLong()
            adjList[from].add(Edge(to,cost))
            adjList[to].add(Edge(from,cost))
        }
        adjList.map { it.toList() }
    }

    // root を根とした根付き木を返す。
    fun makeRootedTree(root: Int): LongArray{
        val parent = IntArray(N+1){-1}
        val dist = LongArray(N+1){-1}
        dist[root] = 0L
        dfs(root, parent, dist)
        return dist
    }

    fun dfs(v: Int, parent: IntArray, dist: LongArray) {
        adj[v].filter { dist[it.to]==-1L }.forEach {
            parent[it.to] = v
            dist[it.to] = dist[v] + it.cost
            dfs(it.to, parent, dist)
        }
    }
}