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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(dead_code)]

use proconio::input;
use proconio::marker::{Bytes, Chars};
use std::collections::*;

fn main() {
    input! {
        n:usize,
        abc:[(usize,usize,i64);n-1],
        q:usize,
        k:usize,
        xy:[(usize,usize);q],
    }
    let mut g = Graph::new(n);
    for e in abc {
        g.add_undirectional_edge(e.0 - 1, e.1 - 1, e.2);
    }
    let dist = bfs(&g, k - 1);
    let xy = xy.iter().map(|&(x, y)| (x - 1, y - 1)).collect::<Vec<_>>();
    for (x, y) in xy {
        let ans = dist[x] + dist[y];
        println!("{}", ans);
    }
}

fn bfs(g: &Graph, k: usize) -> Vec<i64> {
    let mut res = vec![std::i64::MAX; g.len()];
    res[k] = 0;
    let mut b = VecDeque::new();
    b.push_back(k);
    while let Some(now) = b.pop_front() {
        for next in g[now].iter() {
            if res[next.to] != std::i64::MAX {
                continue;
            }
            res[next.to] = res[now] + next.cost;
            b.push_back(next.to);
        }
    }
    return res;
}

#[derive(Debug, Copy, Clone)]
pub struct Edge {
    pub to: usize,
    pub cost: i64,
}
impl Edge {
    pub fn new(to: usize, cost: i64) -> Edge {
        Edge { to: to, cost: cost }
    }
}
pub struct Graph {
    adjacency: Vec<Vec<Edge>>,
}
impl Graph {
    pub fn new(size: usize) -> Self {
        Graph {
            adjacency: vec![vec![]; size],
        }
    }
    pub fn len(&self) -> usize {
        self.adjacency.len()
    }
    pub fn add_directional_edge(&mut self, from: usize, to: usize, cost: i64) {
        self.adjacency[from].push(Edge::new(to, cost));
    }
    pub fn add_undirectional_edge(&mut self, from: usize, to: usize, cost: i64) {
        self.add_directional_edge(from, to, cost);
        self.add_directional_edge(to, from, cost);
    }
}
impl std::ops::Index<usize> for Graph {
    type Output = Vec<Edge>;
    fn index(&self, vertex: usize) -> &Self::Output {
        &self.adjacency[vertex]
    }
}