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.*
import java.io.*

val pw = PrintWriter(System.out)
val MOD = 1000000007L
val INF = 2147483647
val LINF = 9223372036854775807L

fun main(args: Array<String>){
    solve()
    pw.flush()    
}

fun solve(){
    val n = nextInt()
    val nodes: Array<Node> = Array(n) { Node(it) }
    repeat(n - 1){
        val (a, b, c) =nextIntList()
        nodes[a - 1].edges.add(Edge(a - 1, b - 1, c.toLong()))
        nodes[b - 1].edges.add(Edge(b - 1, a - 1, c.toLong()))
    }

    val (q, k) = nextIntList()
    val dist = dijkstra(nodes, k - 1)
    val ans = Array(q) { 0L }
    repeat(q) { 
        val (x, y) = nextIntList()
        ans[it] = dist[x - 1] + dist[y - 1]
    }

    for (i in ans) {
        println(i)
    }

}

fun dijkstra(nodes: Array<Node>, start: Int) : Array<Long> {
    val queue = PriorityQueue<Edge>(16) { e1: Edge, e2: Edge ->
        if(e1.cost < e2.cost){
            return@PriorityQueue -1
        } else if (e2.cost > e1.cost) {
            return@PriorityQueue 1
        } else {
            return@PriorityQueue 0
        }
    }
    queue.add(Edge(start, start, 0))
    val dist: Array<Long> = Array(nodes.size) { LINF / 2 }
    dist[start] = 0
    while(queue.isNotEmpty()){
        val now = queue.poll()
        if(dist[now.to] < now.cost) continue;
        for (edge in nodes[now.to].edges) {
            if(dist[edge.to] <= dist[edge.from] + edge.cost) continue
            dist[edge.to] = dist[edge.from] + edge.cost
            queue.add(Edge(edge.from, edge.to, dist[edge.to]))
            nodes[edge.to].past = edge.from
        }
    }
    return dist
}

// Print
fun println(v: String){
    pw.println(v)
}
fun print(v: String){
    pw.print(v)
}

// Read
fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ").toMutableList()
fun nextIntList(index: Int = 0) = next().split(" ").map{ it.toInt() + index }.toMutableList()
fun nextLongList(index: Long = 0L) = next().split(" ").map{ it.toLong() + index }.toMutableList()
fun nextDoubleList() = next().split(" ").map{ it.toDouble() }.toMutableList()
fun nextAryln(n: Int) = Array(n){ next() }
fun nextIntAryln(n: Int, index: Int = 0) = IntArray(n){ nextInt() + index }
fun nextLongAryln(n: Int, index: Long = 0) = LongArray(n){ nextLong() + index }
fun nextDoubleAryln(n: Int) = DoubleArray(n) { nextDouble() }

// Array
fun ary(n: Int, init: String = "") = Array(n) { init }
fun intAry(n: Int, init: Int = 0) = IntArray(n) { init }
fun longAry(n: Int, init: Long = 0L) = LongArray(n) { init }
fun doubleAry(n: Int, init: Double = 0.0) = DoubleArray(n) { init }
fun ary2(n: Int, m: Int, init: String = "") = Array(n) { Array(m) { init } }
fun intAry2(n: Int, m: Int, init: Int = 0) = Array(n) { IntArray(m) { init } }
fun longAry2(n: Int, m: Int, init: Long = 0) = Array(n) { LongArray(m) { init } }
fun doubleAry2(n: Int, m: Int, init: Double = 0.0) = Array(n) { DoubleArray(m) { init } }
fun ary3(n: Int, m: Int, k: Int, init: String = "") = Array(n) { Array(m) { Array(k) { init } } }
fun intAry3(n: Int, m: Int, k: Int, init: Int = 0) = Array(n) { Array(m) { IntArray(k) { init } } }
fun longAry3(n: Int, m: Int, k: Int, init: Long = 0L) = Array(n) { Array(m) { LongArray(k) { init } } }
fun doubleAry3(n: Int, m: Int, k: Int, init: Double = 0.0) = Array(n) { Array(m) { DoubleArray(k) { init } } }


// Math
fun abs(n: Int) : Int = Math.abs(n)
fun abs(n: Long) : Long = Math.abs(n)
fun abs(n: Double) : Double = Math.abs(n)
fun max(a: Int = -INF, b: Int = -INF, c: Int = -INF, d: Int = -INF, e: Int = -INF): Int = listOf(a, b, c, d, e).max()!!
fun max(a: Long = -LINF, b: Long = -LINF, c: Long = -LINF, d: Long = -LINF, e: Long = -LINF): Long = listOf(a, b, c, d, e).max()!!.toLong()
fun min(a: Int = INF, b: Int = INF, c: Int = INF, d: Int = INF, e: Int = INF): Int = listOf(a, b, c, d, e).min()!!
fun min(a: Long = LINF, b: Long = LINF, c: Long = LINF, d: Long = LINF, e: Long = LINF): Long = listOf(a, b, c, d, e).min()!!.toLong()
fun prime(from: Long, to: Long = from) : List<Long>{
    return (from..to).filter{ i ->
        val max = Math.sqrt(i.toDouble()).toLong()
        (2..max).all{ j -> i % j != 0L}
    }
}
fun gcd(a: Long, b: Long) : Long = if(a % b == 0L) b else gcd(b, (a % b))
fun lcm(a: Long, b: Long) : Long = a / gcd(a, b) * b
fun modpow(a: Long, n: Long, p:Long = MOD) : Long {
    var res = 1L
    var ar = a
    var nr = n
    while(nr > 0){
        if((nr and 1) == 1L) res = res * ar % p
        ar = ar * ar % p
        nr = nr shr 1
    }
    return res
}
fun modinv(a: Long, p: Long = MOD) : Long = modpow(a, p - 2, p)
fun ncr(n: Long, r: Long) : Long {
    var a = 1L
    var b = 1L
    for (i in 1..r) {
        a = a * (n + 1 - i) % MOD
        b = b * i % MOD
    }
    return modinv(b, MOD) * a % MOD
}

class Permutation(val n: Int, var searched: Int = 0, var nextIndex: Int = 0){
    val size = fact(n)
    val permList = Array(size) { IntArray(n){ 0 } }

    fun fact(n: Int) : Int = if(n == 0) 1 else n * fact(n - 1)
    fun init(){
        create(0, IntArray(n) { 0 }, Array<Boolean>(n){ false })
    }
    fun create(num: Int, list: IntArray, flag: Array<Boolean>){
        if(num == n){
            permList[searched] = list.copyOf()
            searched++
        }
        for (i in 0 until n) {
            if(flag[i]) continue
            list[num] = i
            flag[i] = true
            create(num + 1, list, flag)
            flag[i] = false
        }
    }
    fun hasNext() : Boolean {
        if(nextIndex < size){
            return true
        } else {
            nextIndex = 0
            return false
        }
    }
    fun nextPerm() : IntArray = permList[nextIndex++]
}

data class Node(val id: Int, var past: Int = -1, var edges: MutableList<Edge> = mutableListOf())
data class Edge(val from: Int, val to: Int, val cost: Long = 1L)