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 9.2.1) (judge verdict: Runtime Error)

#include <iostream>
#include <iomanip>
#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <utility>
#include <cmath>
#include <tuple>
#include <queue>
#include <bitset>
#include <set>
#include <map>
#include <list>

using ll = long long;
using ld = long double;
using namespace std;
const int INF = 1e9+100;
const ll INF64 = 7e18l;
const int mod = 1000000007;
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define ALL(a) (a).begin(), (a).end()
#define FIN ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);

using Graph = vector<vector<ll>>;

int main(){
    FIN;
    ll n; cin >> n;
    vector<vector<ll>> c(n,vector<ll>(n,0));
    Graph G(n);
    for(ll i=0;i<n-1;i++){
        ll a,b;
        cin >> a >> b;
        a--; b--;
        ll C;
        cin >> C;
        c[a][b] = C;
        c[b][a] = C;
        G[a].push_back(b);
        G[b].push_back(a);
    }

    ll q,k;
    cin >> q >> k;
    k--;
    vector<ll> ans(q);

    for(ll i=0;i<q;i++){
        ll x,y;
        cin >> x >> y;
        x--; y--;

        vector<ll> dist(n,-1);
        queue<ll> que;

        dist[k] = 0;
        que.push(k);

        while(!que.empty()){
            ll v = que.front();
            que.pop();

            for(ll nv : G[v]){
                if(dist[nv] != -1) continue;

                dist[nv] = dist[v] + c[v][nv];
                que.push(nv);
            }
        }

        ans[i] = dist[x] + dist[y];
    }

    for(int i=0;i<q;i++) cout << ans[i] << endl;
    return 0;
}