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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
#define ll long long

vector<ll> distances;

void bfs(ll start, vector<vector<pair<ll,ll>>> &adjlist) {
	//returns all distances to start`
	queue<pair<ll,ll>> q;
	q.push({start,0});
	while (!q.empty()) {
		ll v = q.front().first, c = q.front().second;
		distances[v] = c;
		q.pop();
		for (pair<ll,ll> p : adjlist[v]) {
			ll nextv = p.first, nextc = p.second;
			if (!distances[nextv])
				q.push({nextv,c+nextc});
		}
	}
	distances[start]=0;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	ll n; cin>>n;
	vector<vector<pair<ll,ll>>> adjlist(n+1);
	distances.resize(n+1);
	for (ll i=0; i<n-1; i++) {
		ll a,b,c; cin>>a>>b>>c;
		adjlist[a].push_back({b,c});
		adjlist[b].push_back({a,c});
	}

	ll q,k; cin>>q>>k;
	bfs(k,adjlist);
	while (q--) {
		ll x,y; cin>>x>>y;
		cout << distances[x] + distances[y] << endl;
	}
	return 0;
}