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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdbool.h>

int n,q,k;
int m,head[300020],next[300020],to[300020];
long long len[300020],dis[300020];
bool visited[300020];

void dfs(int x,int y, long long d){
    dis[x]=d;
    visited[x]=true;
    for (int e=head[x]; e!=-1; e=next[e]){
        if (visited[to[e]]==false){
           if (to[e]==y) {
                continue;
            }
            dfs(to[e],x,len[e]+d);
            visited[to[e]]=false;
        }
    }
}

int main(void){
    scanf("%d",&n);
    for (int i=0; i<n; i++){
        head[i]=-1;
    }
    for (int i=0; i<n-1; i++){
        int a,b;
        long long c;
        scanf("%d%d%lld",&a,&b,&c);
        a--;
        b--;
        next[m]=head[a];
        head[a]=m;
        to[m]=b;
        len[m]=c;
        m++;
        next[m]=head[b];
        head[b]=m;
        to[m]=a;
        len[m]=c;
        m++;
    }
    scanf("%d%d",&q,&k);
    dfs(k-1,-1,0);
    for (int i=0; i<q; i++){
        int x,y;
        scanf("%d%d",&x,&y);
        printf("%lld\n",dis[x-1]+dis[y-1]);
    }
	return 0 ;
}