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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

void dfs(vector<vector<int>> const& adj, vector<vector<int64_t>> const& costs, int k, int v, vector<int64_t>& result)
{
    for (int ichild = 0; ichild < (int) adj[v].size(); ++ichild) {
        int child = adj[v][ichild];
        int64_t cost = costs[v][ichild];
        if (!result[child] && child != k) {
            result[child] = result[v] + cost;
            dfs(adj, costs, k, child, result);
        }
    }
}

int main()
{
    cin.sync_with_stdio(false); cin.tie(0);
    cout.sync_with_stdio(false); cout.tie(0);

    int n;
    cin >> n;
    vector<vector<int>> adj(n);
    vector<vector<int64_t>> costs(n);
    for (int i = 0; i < n - 1; ++i) {
        int x, y; int64_t cost;
        cin >> x >> y >> cost; --x; --y;
        adj[x].push_back(y);
        adj[y].push_back(x);
        costs[x].push_back(cost);
        costs[y].push_back(cost);
    }
    vector<int64_t> result(n);
    int q, k;
    cin >> q >> k; --k;
    dfs(adj, costs, k, k, result);
    for (int i = 0; i < q; ++i) {
        int x, y;
        cin >> x >> y; --x; --y;
        cout << result[x] + result[y] << "\n";
    }
}