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<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<cstdlib>
#include <cmath>
#include<stdio.h>
#include<queue>
#include<stack>
#include<set>
#define MAX 1000000000000000000LL
long long inf=100000000000007;
using namespace std;
struct edge{long long to,cost;};
typedef pair<int,int>P;
vector<edge> G[100005];
long long d[100005];
int n;

void dijkstra(long long k){
    priority_queue<P,vector<P>,greater<P> >que;
    fill(d,d+n,inf);
    d[k]=0;
    que.push(P(0,k));
    while(!que.empty()){
        P p=que.top();que.pop();
        int v=p.second;
        if(d[v]<p.first)continue;
        for(int i=0;i<G[v].size(); i++){
            edge e=G[v][i];
            if(d[e.to]>d[v]+e.cost){
                d[e.to]=d[v]+e.cost;
                que.push(P(d[e.to],e.to));
            }
        }
    }
}

int main(){
    cin>>n;
    long long  a,b,c;
    for(int i=0; i<n-1; i++){
        cin>>a>>b>>c;
        a--;b--;
        G[a].push_back(edge{b,c});
        G[b].push_back(edge{a,c});
    }
    long long q,k;
    cin>>q>>k;
    dijkstra(k-1);
    long long st,go;
    for(int i=0; i<q; i++){
        cin>>st>>go;
        st--;go--;
        cout<<d[st]+d[go]<<endl;
    }
    return 0;
}