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: Runtime Error)

#include <stdio.h>
#include <stdlib.h>

long long int inf=1000000000000000000;

long long int Change(int x,int K,long long int **C,int N){
	long long int ans=inf;
	long long int new_ans; 
	int i;
	if (C[x-1][K-1]!=inf){
		long long int ans=C[x-1][K-1];
		return ans;
	}
	else {
		for (i=0;i<N;i++){
			if (C[x-1][i]!=inf&&C[x-1][i]!=-1){
				long long int t=C[x-1][i];
				C[x-1][i]=C[i][x-1]=-1;
				new_ans=t+Change(i,K,C,N);
				if (new_ans<ans){
					ans=new_ans;
				}
				C[x-1][i]=C[i][x-1]=t;
			}
		}
		return ans;
	}
}

int main(){
	int N;
	scanf("%d",&N);
	long long int **C=malloc(N*sizeof(long long int*));
	int a,b;
	long long int c;
	int i,j,k;
	for (i=0;i<N;i++){
		C[i]=malloc(N*sizeof(long long int));
		for (j=0;j<N;j++){
			C[i][j]=inf;
		}
	}
	for (i=0;i<N-1;i++){
		scanf("%d %d",&a,&b);
		scanf("%lld",&c);
		C[a-1][b-1]=C[b-1][a-1]=c;
	}
	for (i=0;i<N;i++){
		for (j=0;j<N;j++){
			for (k=0;k<N;k++){
				if (C[i][j]>C[i][k]+C[k][j]){
					C[i][j]=C[i][k]+C[k][j];
				}
			}
		}
	}

	int Q,K;
	int x,y;
	scanf("%d %d",&Q,&K);

	for (i=0;i<Q;i++){
		scanf("%d %d",&x,&y);
		C[x-1][K-1]=C[K-1][x-1]=Change(x,K,C,N);
		C[y-1][K-1]=C[K-1][y-1]=Change(y,K,C,N);
		long long int ans=C[x-1][K-1]+C[y-1][K-1];
		printf("%lld\n",ans);
	}
	return 0;
}