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 <limits.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
#include <math.h>

#define P 1000000007

int comp(const void *a, const void *b){return *(int*)a-*(int*)b;}

int e[200000][3];
long d[100001];
int search(int x, int l, int r){
	while(l<=r){
		int m=(l+r)/2;
		if(e[m][0]>=x) r=m-1; else l=m+1;
	}
	return l;
}

int main(void){
	int n, k, q, i;
	scanf("%d", &n);
	for(i=0; i<n-1; i++){
		int A, B, C;
		scanf("%d%d%d", &A, &B, &C);
		e[i*2][0]=A; e[i*2][1]=B; e[i*2][2]=C;
		e[i*2+1][0]=B; e[i*2+1][1]=A; e[i*2+1][2]=C;
	}
	scanf("%d%d", &q, &k);
	qsort(e, (n-1)*2, sizeof(int)*3, comp);

	int s[100000], S=0;
	d[k]=0;
	s[S++]=k;
	while(S>0){
		int p=s[--S];
		i=search(p, 0, (n-1)*2-1);
		for(; e[i][0]==p; i++){
			if(d[e[i][1]]==0){
				d[e[i][1]] = d[p] + e[i][2];
				s[S++]=e[i][1];
			}
		}
	}
	d[k]=0;

	for(i=0; i<q; i++){
		int x, y;
		scanf("%d%d", &x, &y);
		printf("%ld\n", d[x]+d[y]);
	}
}