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>

typedef struct {
	int end[2];
	long long cost;
} edge;

typedef struct List {
	struct List *next;
	edge *f;
} list;

int main()
{
	int i, N, Q, K, a[100001], b[100001], x[100001], y[100001];
	long long c[100001];
	scanf("%d", &N);
	for (i = 1; i <= N - 1; i++) scanf("%d %d %lld", &(a[i]), &(b[i]), &(c[i]));
	scanf("%d %d", &Q, &K);
	for (i = 1; i <= Q; i++) scanf("%d %d", &(x[i]), &(y[i]));
	
	edge e[100001];
	list *inc[100001] = {}, l[200001];
	for (i = 1; i <= N - 1; i++) {
		e[i].end[0] = a[i];
		e[i].end[1] = b[i];
		e[i].cost = c[i];
		l[(i-1)*2].f = &(e[i]);
		l[(i-1)*2+1].f = &(e[i]);
		l[(i-1)*2].next = inc[a[i]];
		l[(i-1)*2+1].next = inc[b[i]];
		inc[a[i]] = &(l[(i-1)*2]);
		inc[b[i]] = &(l[(i-1)*2+1]);
	}
	
	int flag[100001] = {}, q[100001] = {K}, head, tail;
	long long dist[100001] = {};
	flag[K] = 1;
	list *p;
	for (head = 0, tail = 1; head < tail; head++) {
		for (p = inc[q[head]]; p != NULL; p = p->next) {
			i = (p->f->end[0] == q[head])? p->f->end[1]: p->f->end[0];
			if (flag[i] == 0) {
				flag[i] = 1;
				dist[i] = dist[q[head]] + p->f->cost;
				q[tail++] = i;
			}
		}
	}
	
	for (i = 1; i <= Q; i++) printf("%lld\n", dist[x[i]] + dist[y[i]]);
	fflush(stdout);
	return 0;
}