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>
#define rep(i,n,m) for(int i = (n); i <(m); i++)
using namespace std;
using ll = long long;
using pii = pair<int, int>;
const int LOGN = 20;
const int MAXN = 100010;

ll dis[MAXN];
int parent[MAXN][LOGN];
vector<pii> edges[MAXN];

void dfs(int node)
{
    rep(i, 0, MAXN) dis[i] = -1;

    queue<int> que;
    que.push(node);
    dis[node] = 0;

    while (que.size() > 0)
    {
        int node = que.front();
        ll d = dis[node];
        que.pop();

        for (auto next_c : edges[node])
        {
            int next = next_c.first;
            ll c = next_c.second;

            if (dis[next] != -1) continue;

            que.push(next);
            dis[next] = d + c;
        }
    }
};


int main()
{
    int n;
    cin >> n;
    rep(i, 0, n - 1)
    {
        int a, b, c;
        cin >> a >> b >> c;
        a--, b--;
        edges[a].emplace_back(b, c);
        edges[b].emplace_back(a, c);
    }


    int q, k;
    cin >> q >> k;
    k--;

    dfs(k);

    rep(i, 0, q)
    {
        int x, y;
        cin >> x >> y;
        x--, y--;

        cout << dis[x] + dis[y] << endl;
    }
    return 0;
}