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 <string>
#include <queue>
#include <stack>
#include <vector>
#include <sstream>
#include <algorithm>
#include <deque>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <list>
#include <cstdio>
#include <iostream>
#include <cmath>
#include <climits>
#include <bitset>
#include <functional>
#include <numeric>
#include <ctime>
#include <cassert>
#include <cstring>
#include <fstream>

#define rep(i, a, b) for(int (i)=(a); (i)<(b); (i)++)
#define irep(i, a, b) for(int (i)=(a);(i)<=(b);(i)++)
#define rrep(i, a, b) for(int (i)=(a);(i)>=(b);(i)--)

using namespace std;

const int MOD = 1e9 + 7;

struct Edge {
    int to;
    long long cost;
};

void calc_depth(int node, int from,  vector<long long> &depth, vector<vector<Edge>> &edges) {
    for (auto t : edges[node]) {
        int to = t.to;
        if (to == from)
            continue;
        depth[to] = depth[node] + t.cost;
        calc_depth(to, node, depth, edges);


    }
}

int main() {
    int n;
    cin >> n;

    vector<int> a(n - 1), b(n - 1), c(n - 1);
    rep(i, 0, n - 1) {
        cin >> a[i] >> b[i] >> c[i];
        a[i]--, b[i]--;
    } 
    vector<vector<Edge>> edges(n);
    rep(i, 0, n - 1) {
        edges[a[i]].push_back({ b[i], c[i] });
        edges[b[i]].push_back({ a[i], c[i] });
    }
    int q, k;
    cin >> q >> k;
    k--;

    vector<long long> depth(n);
    depth[k] = 0;
    calc_depth(k, -1, depth, edges);


    rep(i, 0, q) {
        int x, y;
        cin >> x >> y;
        x--, y--;
        cout << depth[x] + depth[y] << endl;
        
    }
   
    return 0;
}