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: Runtime Error)

// AtCoder template
#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i = 0; i < n; ++i)
typedef long long ll;


struct node{
    node(int n,ll d){
        num = n;
        cost = d;
    }
    int num;
    ll cost;
};
vector<vector<struct node>> graph(10001);

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

    int n; cin >> n;
    int a,b; ll c; rep(i,n-1){
        cin >> a >> b >> c;
        a--; b--;
        graph[a].emplace_back(b,c);
        graph[b].emplace_back(a,c); // how?
    }


    int Q, K; cin >> Q >> K;
    vector<ll> k_dist(n,-1);    
    queue<pair<int,ll>> q;
    q.emplace(K-1,0);

    while(!q.empty()){
        int now = q.front().first;
        ll dist = q.front().second;
        q.pop();
        k_dist[now] = dist;

        rep(i,graph[now].size()){
            int next = graph[now][i].num;
            if(k_dist[next] != -1) continue;
            q.emplace(next, dist+graph[now][i].cost);
        }
    }

    int x,y;
    rep(i,Q){
        cin >> x >> y;
        x--; y--;
        cout << k_dist[x] + k_dist[y] << "\n";
    }
}