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)

fun main(arg: Array<String>) {
    val INF = 1L.shl(40)
    val N = nextInt()
    val G = Array(N) { mutableListOf<Pair<Int, Long>>() }
    repeat(N - 1) {
        val (a, b, c) = listOfInt(-1, -1, 0)
        val C = c.toLong()
        G[a].add(b to C); G[b].add(a to C)
    }
    val Cs = hashMapOf<Pair<Int, Int>, Long>()
    fun get(x: Int, y: Int): Long {
        val cs = Cs.getOrElse(x to y, { INF })
        if (cs < INF) return cs

        val V = BooleanArray(N)
        fun dfs(s: Int, c: Long, L: Int): Long {
            if (s == y) return c
            if (V[s]) return INF
            V[s] = true
            var cc = INF
            for (d in G[s]) {
                cc = Math.min(cc, dfs(d.first, c + d.second, L + 1))
            }
            return cc
        }
        val rtn = dfs(x, 0, 0)
        Cs.set(x to y, rtn)
        return rtn
    }
    val (Q, K) = listOfInt(0, -1)
    val ans = LongArray(Q)
    repeat(Q) { q ->
        val (x, y) = listOfInt(-1, -1)
        ans[q] = get(x, K) + get(K, y)
    }
    println(ans.joinToString("\n"))
}
fun gcd(a: Long, b: Long): Long = if (b > 0) gcd(b, a % b) else a
fun lcm(a: Long, b: Long): Long = a / gcd(a, b) * b
fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun listOfString() = next().split(" ")

fun listOfInt(vararg deltas: Int) = listOfString().map { Integer.parseInt(it) }.mapIndexed { index, int -> int + deltas[index % deltas.size] }