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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::*;

fn dijkstra(start: usize, graph: &Vec<Vec<(usize, i64)>>) -> Vec<i64> {
    let mut dist = vec![std::i64::MAX; graph.len()];
    dist[start] = 0;
    let mut bh = std::collections::BinaryHeap::new();
    bh.push((0i64, start));
    while let Some((cost, v)) = bh.pop() {
        if dist[v] < -cost {
            continue;
        }
        for e in graph[v].iter() {
            let nv = e.0;
            let nc = e.1;
            if dist[nv] > -cost + nc {
                dist[nv] = -cost + nc;
                bh.push((-dist[nv], nv));
            }
        }
    }
    dist
}

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();

    let mut graph: Vec<Vec<(usize, i64)>> = vec![Vec::new(); n];
    for _ in 0..n - 1 {
        let a: usize = itr.next().unwrap().parse::<usize>().unwrap() - 1;
        let b: usize = itr.next().unwrap().parse::<usize>().unwrap() - 1;
        let c: i64 = itr.next().unwrap().parse().unwrap();
        graph[a].push((b, c));
        graph[b].push((a, c));
    }
    let q: usize = itr.next().unwrap().parse().unwrap();
    let k: usize = itr.next().unwrap().parse().unwrap();
    let dist = dijkstra(k - 1, &graph);
    let mut out = Vec::new();
    for _ in 0..q {
        let x: usize = itr.next().unwrap().parse::<usize>().unwrap() - 1;
        let y: usize = itr.next().unwrap().parse::<usize>().unwrap() - 1;
        writeln!(out, "{}", dist[x] + dist[y]).ok();
    }
    stdout().write_all(&out).unwrap();
}