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 <stdlib.h>
#include <string.h>
#include <math.h>
#include <limits.h>
#define swap(type,a,b) do{type t=a;a=b;b=t;}while(0);
#define MAX(a,b) (((a)>(b))?(a):(b))
#define MIN(a,b) (((a)<(b))?(a):(b))
#define ll long long
#define INF (1e+18)
#define FOR(i,a,n) for(i=(a);i<(n);i++)
int comp(const void* a,const void* b){
	return *(int*)a-*(int*)b;
}
void fill(int a[],int b,int c){
	int i;
	FOR(i,0,b) a[i]=c;
	return;
}
typedef struct LIST{
	int to,cost;
	struct LIST *next;
}Edge;
Edge** init(int v){
	Edge **edge=(Edge**)calloc(v,sizeof(Edge*));
	return edge;
}
void add_edge(Edge **edge,int s,int t,int c){
	Edge *tmp=(Edge*)malloc(sizeof(Edge));
	tmp->to=t,tmp->cost=c;
	tmp->next=edge[s];
	edge[s]=tmp;
	return;
}
void delete_edge(Edge **edge,int v){
	int i;
	Edge *e,*tmp;
	FOR(i,0,v){
		e=edge[i];
		while(e!=NULL){
			tmp=e->next;
			free(e);
			e=tmp;
		}
	}
	return;
}
ll d[100000];
Edge **edge;
void dfs(int v,ll dist){
	d[v]=dist;
	for(Edge *e=edge[v];e!=NULL;e=e->next){
		if(d[e->to]==INF) dfs(e->to,dist+e->cost);
	}
	return;
}
int main(void)
{
	int n,a,b,c,q,k,i;
	scanf("%d",&n);
	edge=init(n);
	FOR(i,0,n-1){
		scanf("%d%d%d",&a,&b,&c);
		a--,b--;
		add_edge(edge,a,b,c);
		add_edge(edge,b,a,c);
	}
	FOR(i,0,n) d[i]=INF;
	scanf("%d%d",&q,&k);
	dfs(--k,0LL);
	FOR(i,0,q){
		scanf("%d%d",&a,&b);
		printf("%lld\n",d[--a]+d[--b]);
	}
	delete_edge(edge,n);
	return 0;
}