题目描述
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.
Input
<dl> <dt>Input is given from Standard Input in the following format:</dt> <dt>N</dt> <dt>a_1 b_1 c_1</dt> <dd> <dl> <dt>a_{N-1} b_{N-1} c_{N-1}</dt> <dt>Q K</dt> <dt>x_1 y_1</dt> <dd>x_{Q} y_{Q}</dd> </dl> </dd> </dl>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.
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)
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
输入格式
见题面 Input 部分
输出格式
见题面 Output 部分