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: Time Limit Exceeded)

import java.io.*
import java.util.*

var pw = PrintWriter(System.out)
fun solve(N: Int, a: IntArray, b: IntArray, c: LongArray, Q: Int, K: Int, x: IntArray, y: IntArray){
    val tree = AdjacentListGraph<Int, Long>(Array(N){ Vertex<Int, Long>() }.toMutableList())
    for(i in 0 until N - 1){
        tree.addEdge(a[i] - 1, b[i] - 1, c[i])
        tree.addEdge(b[i] - 1, a[i] - 1, c[i])
    }
    val distances = tree.getDistances(K - 1)
    // println(distances.toList())
    repeat(Q){
        val ans = distances[x[it] - 1] + distances[y[it] - 1]
        pw.println(ans)
    }
    pw.flush()
    return
}

fun AdjacentListGraph<Int, Long>.getDistances(from: Int): LongArray{
    // Breadth First Search
    val distances = LongArray(vertices.size){ -1L }
    distances[from] = 0
    val queue = ArrayDeque<Int>()
    queue.add(from)
    while(queue.size > 0){
        val node = queue.removeFirst()
        val curDist = distances[node]
        vertices[node].edges.filter{ distances[it.to] == -1L }.forEach{
            val delta = it.weight?: 1L
            distances[it.to] = curDist + delta
            queue.add(it.to)
        }
    }
    return distances
}
data class Vertex<T : Comparable<T>, E : Comparable<E>>(val data: T? = null) {
    data class Edge<T : Comparable<T>>(val to: Int, val weight: T? = null)

    val edges = mutableListOf<Edge<E>>()

    fun addEdge(to: Int, weight: E?) = when (edges.find { it.to == to }) {
        null -> {
            edges.add(Edge(to, weight))
            true
        }
        else -> false
    }

    fun removeEdge(to: Int): Boolean{
        for ((i, edge) in edges.withIndex()){
            if (edge.to == to){
                edges.removeAt(i)
                return true
            }
        }
        return false
    }
}

class AdjacentListGraph<T : Comparable<T>, E : Comparable<E>>(
    val vertices: MutableList<Vertex<T, E>>
) {
    // T = data of Vertex, E = weight of Edge
    fun getWeight(from: Int, to: Int): E? = vertices[from].edges.find { it.to == to }?.weight
    fun addEdge(from: Int, to: Int, weight: E? = null) = vertices[from].addEdge(to, weight)
    fun removeEdge(from: Int, to: Int) = vertices[from].removeEdge(to)
    fun isAdjacent(from: Int, to: Int) = vertices[from].edges.find { it.to == to } != null
}

fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }
    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }
    val sc = Scanner(System.`in`)
    val N = sc.next().toInt()
    val a = IntArray(N-1)
    val b = IntArray(N-1)
    val c = LongArray(N-1)
    for (i in 0 until N-1) {
        a[i] = sc.next().toInt()
        b[i] = sc.next().toInt()
        c[i] = sc.next().toLong()
    }
    val Q = sc.next().toInt()
    val K = sc.next().toInt()
    val x = IntArray(Q.toInt())
    val y = IntArray(Q.toInt())
    for (i in 0 until Q.toInt()) {
        x[i] = sc.next().toInt()
        y[i] = sc.next().toInt()
    }
    solve(N, a, b, c, Q, K, x, y)
}