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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
)

var sc = NewScanner(os.Stdin, 1000000)

var (
	n, q, k    int
	lenMap     [][]int
	refMap     [][]int
	visitedMap []bool
)

func initVisitedMap() {
	visitedMap = make([]bool, n+1)
}

func search(curr, goal int, dist uint64) uint64 {
	if curr == goal {
		return dist
	}
	result := uint64(0)
	for _, next := range refMap[curr] {
		if visitedMap[next] == true {
			return uint64(0)
		}
		visitedMap[next] = true
		s := search(next, goal, dist+uint64(lenMap[curr][next]))
		result += s
	}
	return result
}

func main() {
	n = sc.ReadInt()

	lenMap = make([][]int, n+1)
	for i := 0; i < n+1; i++ {
		lenMap[i] = make([]int, n+1)
	}

	refMap = make([][]int, n+1)

	var a, b, c int
	for i := 0; i < n-1; i++ {
		a, b, c = sc.ReadInt(), sc.ReadInt(), sc.ReadInt()
		lenMap[a][b] = c
		lenMap[b][a] = c
		refMap[a] = append(refMap[a], b)
		refMap[b] = append(refMap[b], a)
	}

	q, k = sc.ReadInt(), sc.ReadInt()

	for i := 0; i < q; i++ {
		x, y := sc.ReadInt(), sc.ReadInt()
		initVisitedMap()
		visitedMap[x] = true
		xk := search(x, k, 0)
		initVisitedMap()
		visitedMap[y] = true
		yk := search(y, k, 0)
		fmt.Println(xk + yk)
	}
}

type Scanner struct {
	*bufio.Scanner
}

func (scn *Scanner) ReadInt() int {
	scn.Scanner.Scan()
	i, _ := strconv.Atoi(scn.Scanner.Text())
	return i
}

func NewScanner(r io.Reader, bufSize int) *Scanner {
	buf := make([]byte, bufSize)
	scn := bufio.NewScanner(r)
	scn.Buffer(buf, bufSize)
	scn.Split(bufio.ScanWords)
	return &Scanner{scn}
}