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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad
import qualified Data.Map as M
import qualified Data.IntMap as IM
import Data.List

type Graph = M.Map (Int, Int) Int
type Path = IM.IntMap Int

main :: IO ()
main = do
  n <- readLn :: IO Int
  ns <- replicateM (n - 1) $ do
    [a, b, c] <- getInts
    return [((a, b), c), ((b, a), c)]
  [q, k] <- getInts
  qs <- replicateM q $ do
    [a, b] <- getInts
    return (a, b)
  let graph = M.fromAscList $ sort $ concat ns :: Graph
      path = dfs graph k n
      ans = solve qs path
 -- print path
  mapM_ print ans
  
getInts :: IO [Int]
getInts = map read . words <$> getLine

solve :: [(Int, Int)] -> Path -> [Int]
solve qs path = map f qs
  where
    f (x, y) = path IM.! x + path IM.! y

dfs :: Graph -> Int -> Int -> Path
dfs graph k size = go 0 k 0 IM.empty
  where
    go depth current cost acc
      | depth == size = acc
      | IM.member current acc = acc
      | otherwise =
        let cs = filter ((/= -1) . fst) $
              map (\(a, b) ->
                        case M.lookup (a, b) graph of
                          Nothing -> (-1, -1)
                          Just x -> (b, x))
                 $ zip (repeat current) [1..size] in
          foldl (\acc' (nxt, c') ->
                   go (depth+1) nxt (cost+c')
                                (IM.insert current cost acc')) acc cs