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 <bits/stdc++.h>

using namespace std;

typedef long long int64;

const int64 INF = (1ll << 63) - 1;

vector <vector <pair <int, int> > > g;

vector <int64> dist;

void dijkstra(int s){
    int n = g.size();
    dist.resize(n, INF);
    dist[s] = 0;
    set <pair <int64, int>> v;
    for (int i = 0; i < n; i++){
        v.insert({dist[i], i});
    }
    while(!v.empty()){
        auto it = v.begin();
        int cur_v = it->second;
        int64 cur_v_w = it->first;
        for (int i = 0; i < g[cur_v].size(); i++){
            int nw = g[cur_v][i].first;
            int64 e = g[cur_v][i].second;
            int64 nw_w = cur_v_w + e;
            int64 o_w = dist[nw];
            if (o_w > nw_w){
                v.erase({o_w, nw});
                v.insert({nw_w, nw});
                dist[nw] = nw_w;
            }
        }
        v.erase(v.begin());
    }
}

int main()
{
    #ifdef HOME
    freopen("input.txt", "rt", stdin);
    #endif // HOME
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int n;
    cin >> n;
    g.resize(n);
    for (int i = 0; i < n - 1; i++){
        int a, b;
        int64 c;
        cin >> a >> b >> c;
        a--;
        b--;
        g[a].push_back({b, c});
        g[b].push_back({a, c});
    }
    int q, k;
    cin >> q >> k;
    k--;
    dijkstra(k);
    for (int i = 0; i < q; i++){
        int a, b;
        cin >> a >> b;
        a--;
        b--;
        cout << dist[a] + dist[b] << endl;
    }
    return 0;
}