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 <cstdio>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <string>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <vector>
using namespace std;
#define lowbit(x) ((x)&(-x))
#define INF 0x3f3f3f3f
#define mem(a,b) memset(a,b,sizeof(a))
#define	GE() printf(">----------\n")
#define	IN() freopen("in.txt","r",stdin)
#define	OUT() freopen("out.txt","w",stdout)
#define MP pair<int, int>
typedef long long LL;
const int mod=1000000007;
const LL inf=0x3f3f3f3f3f3f3f3f;
const double pi=acos(-1.0);
const double eps=1e-8;
const int maxn=100005;

int n;
LL dis[maxn];
int inq[maxn];
vector<pair<int, int> > E[maxn];

struct Spfa{

    void init(){
        for(int i=0;i<maxn;i++){
            dis[i]=inf;
            E[i].clear();
            inq[i]=0;
        }
    }

    int spfa(int s){
        queue<int> Q;
        dis[s]=0;
        inq[s]=1;
        Q.push(s);
        while(!Q.empty()){
            int u=Q.front();
            Q.pop();
            inq[u]=0;
            for(int i=0;i<E[u].size();i++){
                int v=E[u][i].first;
                if(dis[v]>dis[u]+E[u][i].second){
                    dis[v]=dis[u]+E[u][i].second;
                    if(inq[v])continue;
                    Q.push(v);
                    inq[v]=1;
                }
            }
        }
        return dis[n];
    }
};

int main()
{
    while(~scanf("%d", &n)){
        Spfa spfa;
        spfa.init();
        int u, v ,w;
        for(int i=0;i<n-1;i++){
            scanf("%d%d%d", &u, &v, &w);
            E[u].push_back(make_pair(v, w));
            E[v].push_back(make_pair(u, w));
        }
        int q, k;
        scanf("%d%d", &q, &k);
        spfa.spfa(k);
        for(int i=0;i<q;i++){
            scanf("%d%d", &u, &v);
            printf("%lld\n", dis[u]+dis[v]);
        }
    }
    return 0;
}