Problem:
Score : 400 points

Problem Statement

Given is a rooted tree with N vertices numbered 1 to N.
The root is Vertex 1, and the i-th edge (1 \leq i \leq N - 1) connects Vertex a_i and b_i.

Each of the vertices has a counter installed. Initially, the counters on all the vertices have the value 0.

Now, the following Q operations will be performed:

Operation j (1 \leq j \leq Q): Increment by x_j the counter on every vertex contained in the subtree rooted at Vertex p_j.

Find the value of the counter on each vertex after all operations.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq Q \leq 2 \times 10^5

1 \leq a_i < b_i \leq N

1 \leq p_j \leq N

1 \leq x_j \leq 10^4

The given graph is a tree.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
a_1 b_1
:
a_{N-1} b_{N-1}
p_1 x_1
:
p_Q x_Q

Output

Print the values of the counters on Vertex 1, 2, \ldots, N after all operations, in this order, with spaces in between.

Sample Input 1

4 3
1 2
2 3
2 4
2 10
1 100
3 1

Sample Output 1

100 110 111 110

The tree in this input is as follows:

Each operation changes the values of the counters on the vertices as follows:

Operation 1: Increment by 10 the counter on every vertex contained in the subtree rooted at Vertex 2, that is, Vertex 2, 3, 4. The values of the counters on Vertex 1, 2, 3, 4 are now 0, 10, 10, 10, respectively.

Operation 2: Increment by 100 the counter on every vertex contained in the subtree rooted at Vertex 1, that is, Vertex 1, 2, 3, 4. The values of the counters on Vertex 1, 2, 3, 4 are now 100, 110, 110, 110, respectively.

Operation 3: Increment by 1 the counter on every vertex contained in the subtree rooted at Vertex 3, that is, Vertex 3. The values of the counters on Vertex 1, 2, 3, 4 are now 100, 110, 111, 110, respectively.

Sample Input 2

6 2
1 2
1 3
2 4
3 6
2 5
1 10
1 10

Sample Output 2

20 20 20 20 20 20

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)


import qualified Data.Vector.Unboxed as U
import qualified Data.Vector as V
import qualified Data.ByteString.Char8 as C
import qualified Data.Array.IO as A
import Debug.Trace
import Data.List
import Control.Monad
import Data.Ord

import qualified Data.IntMap as M
import qualified Data.Sequence as S

import Data.Foldable

r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

rp :: IO (Int,Int)
rp  = toTup . unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

toTup [a,b] = (a,b)


main :: IO ()
main = do
    [n,q] <- r' :: IO [Int]


    ab <- replicateM (n-1) $ do
        [a,b] <- r'
        return (a, S.singleton b)
    
    let mp = M.fromListWith (S.><) ab :: M.IntMap (S.Seq Int)

    px <- replicateM q rp

    let pMap = M.fromListWith (+) px :: M.IntMap Int

    let slMp = solve 1 0 mp pMap
    putStrLn $ intercalate " " $ map (show . snd) (sortBy (comparing fst) $ toList slMp)


solve :: Int -> Int -> M.IntMap (S.Seq Int) -> M.IntMap Int -> S.Seq (Int,Int)
solve pos vac mp pMap =
    let children = case M.lookup pos mp of
                    Just c -> c
                    Nothing -> S.empty
        curVal = case M.lookup pos pMap of
                    Just v -> v
                    Nothing -> 0
        nVal  = curVal + vac
        nacMp = (pos,nVal)
    in -- traceShow (pos,vac,nVal) $
        nacMp S.<| (do  nPos <- children
                        solve nPos nVal mp pMap)