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: Accepted)

import Data.Array.IO
import Data.Int
import qualified Data.ByteString.Char8 as BS
import qualified Data.Vector.Mutable as VM
import Data.Maybe
import Control.Monad

modifyArray arr i f = readArray arr i >>= \x -> writeArray arr i (f x)

bsToNum :: Integral a => BS.ByteString -> a
bsToNum = fromIntegral . fst . fromJust . BS.readInt

main = do
  n <- readLn :: IO Int
  tree <- VM.new n :: IO (VM.IOVector [(Int,Int64)])
  forM_ [0..n-1] $ \i -> VM.write tree i []

  replicateM (n-1) $ do
    (a,b,c) <- BS.getLine >>= return . (\(a:b:c:_) -> (bsToNum a, bsToNum b, bsToNum c)) . BS.words :: IO (Int,Int,Int64)
    VM.read tree (a-1) >>= \x -> VM.write tree (a-1) ((b,c):x)
    VM.read tree (b-1) >>= \x -> VM.write tree (b-1) ((a,c):x)    

  (q:k:_) <- getLine >>= return . map read . words :: IO [Int]

  dist <- VM.new n :: IO (VM.IOVector Int64)
  forM_ [0..n-1] $ \i -> VM.write dist i (-1)

  let
    calc :: Int -> Int -> Int64 -> IO ()
    calc i p d = do
      nodes <- VM.read tree (i-1)
      forM_ nodes $ \(next, c) -> do
        when (next /= p) $ do
          VM.write dist (next-1) (d+c)
          calc next i (d+c)

  VM.write dist (k-1) 0
  calc k (-1) 0

  replicateM q $ do
    (x:y:_) <- BS.getLine >>= return . map bsToNum . BS.words :: IO [Int]
    mapM (VM.read dist) [x-1,y-1] >>= print . sum