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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
#include <functional>
#include <queue>
#include <deque>
#include <string>
#include <stack>
#include <unordered_set>
#include <cmath>
#define endl '\n'
#define ll long long
//#define mod 1000000007
#define NCONS 100001

using namespace std;
int N, Q, K;
vector<ll> adj[NCONS];
vector<ll> cost[NCONS];
bool visited[NCONS];
ll dist[NCONS];

void set_dist(int cur, ll len)
{
	visited[cur] = true;
	dist[cur] = len;
	for (int i = 0; i < adj[cur].size(); i++)
	{
		auto next = adj[cur][i];
		auto next_cost = cost[cur][i];
		if (visited[next]) continue;
		set_dist(next, len + next_cost);
	}
}

int main(void)
{
	cin.tie(NULL); ios_base::sync_with_stdio(false);
	cin >> N;
	for (int i = 0; i < N - 1; i++)
	{
		ll a, b, c; cin >> a >> b >> c;
		adj[a].push_back(b);
		adj[b].push_back(a);
		cost[a].push_back(c);
		cost[b].push_back(c);
	}
	cin >> Q >> K;
	set_dist(K, 0);
	for (int i = 0; i < Q; i++)
	{
		int x, y; cin >> x >> y;
		cout << dist[x] + dist[y] << endl;
	}
	return 0;
}