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: Runtime Error)

import qualified Data.ByteString.Char8 as BC
import Data.Maybe (fromJust)
import Data.List
import Data.Array.IO
import Control.Monad

type Memo = IOUArray (Int, Int) Int

main = do
  n <- readLn :: IO Int
  edge <- (\[x,y,z] -> zip3 x y z) . transpose <$> replicateM (n-1) getIntListBC
  [q, k] <- map read . words <$> getLine :: IO [Int]
  query <- (\[x,y] -> zip x y) . transpose <$> getInt2DListBC
  adjacency <- newArray ((1, 1), (n, n)) (maxBound :: Int) :: IO Memo
  mark <- newArray (1, n) False :: IO (IOUArray Int Bool)
  weight <- newArray (1, n) 0 :: IO (IOUArray Int Int)
  neighbors <- newArray ((1, 0), (n, n-1)) 0 :: IO Memo
  foldM (initEdge neighbors) adjacency edge
  foldM memoize adjacency [1..n]
  kn <- readArray neighbors (k, 0)
  writeArray mark k True
  kNeighbors <- readNeighbors neighbors k kn
  print kNeighbors
  foldM (search adjacency weight neighbors k k) mark kNeighbors
  ans <- mapM (readWeight weight k) query
  print =<< getElems adjacency
  print =<< getElems neighbors
  print =<< getElems weight
  putStrLn . unlines . map show $ ans

bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

getIntListBC :: IO [Int]
getIntListBC = map bsToInt . BC.words <$> BC.getLine

getInt2DListBC :: IO [[Int]]
getInt2DListBC = map (map bsToInt . BC.words) . BC.lines <$> BC.getContents

memoize :: Memo -> Int -> IO Memo
memoize memo i = do
  writeArray memo (i, i) 0
  return memo

initEdge :: Memo -> Memo -> (Int, Int, Int) -> IO Memo
initEdge neighbors memo (x, y, d) = do
  xn <- readArray neighbors (x, 0)
  yn <- readArray neighbors (y, 0)
  writeArray memo (x, y) d
  writeArray memo (y, x) d
  writeArray neighbors (x, 0) $ xn + 1
  writeArray neighbors (y, 0) $ yn + 1
  writeArray neighbors (x, (xn+1)) y
  writeArray neighbors (y, (yn+1)) x
  return memo

--始点k 前pre 現在i
search :: Memo -> IOUArray Int Int -> Memo -> Int -> Int -> IOUArray Int Bool -> Int -> IO (IOUArray Int Bool)
search edge weight neighbors k pre mark i = do
  isMark <- readArray mark i
  case isMark of
    True -> do
      return mark
    False -> do
      writeArray mark i True
      wI <- readArray edge (pre, i)
      wSum <- readArray weight pre
      writeArray weight i (wSum+wI)
      n <- readArray neighbors (i, 0)
      nI <- readNeighbors neighbors i n
      print nI
      return =<< foldM (search edge weight neighbors k i) mark nI

readNeighbors :: Memo -> Int -> Int -> IO [Int]
readNeighbors neighbors i n = mapM (\x -> readArray neighbors (i, x)) [1..n]

readWeight :: IOUArray Int Int -> Int -> (Int, Int) -> IO Int
readWeight weight k (x, y) = do
  kx <- readArray weight x
  ky <- readArray weight y
  return $ kx + ky