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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
from heapq import heappop, heappush
input = sys.stdin.readline

def inp(): # n=1
    return int(input())
def inpm(): # x=1,y=2
    return map(int,input().split())
def inpl(): # a=[1,2,3,4,5,...,n]
    return list(map(int, input().split()))
def inpls(): # a=['1','2','3',...,'n']
    return list(input().split())
def inplm(n): # x=[] 複数行
    return list(int(input()) for _ in range(n))
def inpll(n): # [[1,1,1,1],[2,2,2,2],[3,3,3,3]]
    return sorted([list(map(int, input().split())) for _ in range(n)])
def graphm():
    n=inp()
    g=[[] for _ in range(n)]
    for _ in range(n-1):
        a,b,w=inpm()
        a-=1
        b-=1
        g[a].append((b,w))
        g[b].append((a,w))
    return n,g
def dijkstra(s,to,n,g): # sからの最短距離 頂点数n
    s -= 1
    que = []
    d = [10**15 for _ in range(n)]
    d[s] = 0
    heappush( que,(0,s) )
    while len(que)>0:
        p =  heappop(que)
        v = p[1]
        if d[v] < p[0]:
            if p[1]==to-1:
                break
            continue
        for i in range(len(g[v])):
            edge = g[v][i]
            if d[edge[0]] > d[v] + edge[1]:
                d[edge[0]] = d[v] + edge[1]
                heappush( que,(d[edge[0]] , edge[0]) )
    return d[to-1]

def dijkstra1(s,n,g): # sからの最短距離 頂点数n
    s -= 1
    que = []
    d = [10**15 for _ in range(n)]
    d[s] = 0
    heappush( que,(0,s) )
    while len(que)>0:
        p =  heappop(que)
        v = p[1]
        if d[v] < p[0]:
            continue
        for i in range(len(g[v])):
            edge = g[v][i]
            if d[edge[0]] > d[v] + edge[1]:
                d[edge[0]] = d[v] + edge[1]
                heappush( que,(d[edge[0]] , edge[0]) )
    return d

def main():
    n,graph = graphm()
    q,k = inpm()
    pre = dijkstra1(k,n,graph)
    for _ in range(q):
        x,y = inpm()
        print( dijkstra(x,k,n,graph) + pre[y-1] )    

if __name__ == "__main__":
    main()