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)

-----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-----
5
1 2 1
1 3 1
2 4 1
3 5 1
3 1
2 4
2 3
4 5

-----Sample Output-----
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

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