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 Scala (2.13.1) (judge verdict: Accepted)

import scala.collection.mutable.Stack

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt()
  val e = List.fill(n-1)((sc.nextInt()-1, sc.nextInt()-1, sc.nextLong()))
  val adj = Array.fill(n)(List[(Int, Long)]())
  for ((a, b, c) <- e) {
    adj(a) ::= (b, c)
    adj(b) ::= (a, c)
  }
  val q = sc.nextInt()
  val k = sc.nextInt()-1
  val xy = List.fill(q)((sc.nextInt()-1, sc.nextInt()-1))

  val d = Array.fill(n)(-1L)
  d(k) = 0
  val stack = Stack(k)
  while (stack.nonEmpty) {
    val u = stack.pop()
    for ((v, c) <- adj(u) if d(v) == -1) {
      stack.push(v)
      d(v) = d(u) + c
    }
  }

  val pw = new java.io.PrintWriter(Console.out)
  for ((x, y) <- xy) {
    pw.println(d(x) + d(y))
  }
  pw.flush()
}