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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define nline cout<<"\n"
#define fast ios_base::sync_with_stdio(false)cin.tie(0)
#define ain(A, B, C) assert(IN(A, B, C))
#define ull unsigned long long int
#define ll long long int
#define pii pair<int,int>
#define MAXX 100009
#define fr(a,b,i) for(int i=a;i<b;i++)
#define dbg(x) cout<<"Here we are "<<x<<"\n"
vector<pair<int,int> > G[MAXX];
const int N=100010;
const int LGN=22;
#pragma comment(linker, "/STACK:1000000000")
ll parent[N][LGN],depth[MAXX],vis[MAXX],weight[MAXX];


int uplift(int u,int k){
	for(int i=0;i<LGN;i++){
		if(k&1) u = parent[u][i];
	}
	return u;
}
void dfs(int src){
	vis[src]=1;
	for(int i=0;i<G[src].size();i++){
		int v = G[src][i].first;
		int w = G[src][i].second;
		if(vis[v])continue;
		parent[v][0]=src;
		weight[v]=weight[src]+w;
		depth[v]=depth[src]+1;
		dfs(v);
	}
}
void init(int k)
{
    parent[k][0] = k;
	dfs(k);
		for(int i = 1; i <= N; i++){
            for(int j = 1; j < LGN; j++)
                parent[i][j] = parent[parent[i][j-1]][j-1];
		}

}
int lca(int u,int v){
	int diff=abs(depth[u]-depth[v]);
	if(depth[u]>depth[v]){
		u=uplift(u,diff);
	}
	else if(depth[v]>depth[u]){
		v=uplift(v,diff);
	}
	if(u==v)return u;
	for(int i=LGN-1;i>=0;i--){
		if(parent[u][i]!=parent[v][i]){
			u=parent[u][i];
			v=parent[v][i];
		}
	}

	return parent[u][0];
}
int main()
{
	memset(parent,-1,sizeof parent);
	memset(vis,0,sizeof vis);
	int n;
	cin>>n;
	for(int i=1;i<=n-1;i++){
		int u,v,w;
		cin>>u>>v>>w;
		G[u].pb({v,w});
		G[v].pb({u,w});
	}
	int q, k;
	cin>> q >> k;
	init(k);
	while(q--){
		int a,b;
		cin>>a>>b;
		int lc=lca(a,b);
		if(lc == k){
		ll ans=weight[a]+weight[b]-2*weight[lc];
		   cout << ans << endl;
		}
		else{
           ll ans1 = weight[a]+weight[k]-2*weight[k];
           ll ans2 = weight[k]+weight[b]-2*weight[k];
           ll ans = min(ans1, ans2);
           ll diff = abs(ans1-ans2);
           cout << 2*ans+diff << endl;
		}

	}
	return 0;
}