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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <queue>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <vector>
#define ll long long
#define inf 10000000000000
#define mod 1000000007
using namespace std;
ll read()
{
    ll x=0,f=1;
    char ch=getchar();
    while(ch<'0'||ch>'9')
    {
        if(ch=='-')f=-1;
        ch=getchar();
    }
    while(ch>='0'&&ch<='9')
    {
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x*f;
}
const int N=2e5+10;
const int M=2e5+10;
struct Edge{
    ll cost;
    int to,nxt;
    Edge(){};
    Edge(ll tc,int tt,int tn=0):cost(tc),to(tt),nxt(tn){}
    bool operator < (const Edge &an) const{
        return cost>an.cost;
    }
}Path[M];
int head[N],cnt;
ll dis[N];
bool vis[N];
void Addedge(int u,int v,int w){
    Path[cnt]=(Edge){w,v,head[u]};
    head[u]=cnt++;
}
void Dijkstra(int s,int n)
{
    priority_queue<Edge>que;
    for(int i=1;i<=n;i++) dis[i]=inf;
    dis[s]=0;
    que.push(Edge(0,s));
    while(!que.empty()){
        int cur=que.top().to;que.pop();
        if(vis[cur])continue;
        vis[cur]=true;
        for(int i=head[cur];i;i=Path[i].nxt)
            if(dis[cur]+Path[i].cost<dis[Path[i].to]){
                dis[Path[i].to]=dis[cur]+Path[i].cost;
                que.push(Edge(dis[Path[i].to],Path[i].to));
            }
    }
}
void Init()
{
    memset(head,0,sizeof(head));
    cnt=1;
}
int d2[N];
int main()
{
    int n=read();
    //while(~scanf("%d",&n))
    {
        Init();
        for(int i=2;i<=n;i++){
            int u=read(),v=read(),w=read();
            Addedge(u,v,w);
            Addedge(v,u,w);
        }
        int q=read(),k=read();
        Dijkstra(k,n);
        for(int i=1;i<=q;i++){
            int u=read(),v=read();
            printf("%lld\n",dis[u]+dis[v]);
        }
    }
    return 0;
}