Problem:
Score : 1600 points

Problem Statement

There is a tree with N vertices, numbered 1 through N.
The i-th of the N-1 edges connects vertices a_i and b_i.

Currently, there are A_i stones placed on vertex i.
Takahashi and Aoki will play a game using this tree.

First, Takahashi will select a vertex and place a piece on it.
Then, starting from Takahashi, they will alternately perform the following operation:

Remove one stone from the vertex currently occupied by the piece.

Then, move the piece to a vertex that is adjacent to the currently occupied vertex.

The player who is left with no stone on the vertex occupied by the piece and thus cannot perform the operation, loses the game.
Find all the vertices v such that Takahashi can place the piece on v at the beginning and win the game.

Constraints

2 ≦ N ≦ 3000

1 ≦ a_i,b_i ≦ N

0 ≦ A_i ≦ 10^9

The given graph is a tree.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N
a_1 b_1
:
a_{N-1} b_{N-1}

Output

Print the indices of the vertices v such that Takahashi can place the piece on v at the beginning and win the game, in a line, in ascending order.

Sample Input 1

3
1 2 3
1 2
2 3

Sample Output 1

2

The following is one possible progress of the game when Takahashi places the piece on vertex 2:

Takahashi moves the piece to vertex 1. The number of the stones on each vertex is now: (1,1,3).

Aoki moves the piece to vertex 2. The number of the stones on each vertex is now: (0,1,3).

Takahashi moves the piece to vertex 1. The number of the stones on each vertex is now: (0,0,3).

Aoki cannot take a stone from the vertex, and thus Takahashi wins.

Sample Input 2

5
5 4 1 2 3
1 2
1 3
2 4
2 5

Sample Output 2

1 2

Sample Input 3

3
1 1 1
1 2
2 3

Sample Output 3

Note that the correct output may be an empty line.

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

import Data.Graph.Inductive.Graph
import Data.Graph.Inductive.PatriciaTree
import Control.Monad
import Data.Maybe
import Data.Vector.Unboxed (Vector)
import qualified Data.Vector.Unboxed as V
import Data.List

main = do
  n <- readLn
  as <- map read.words <$> getLine
  edges <- replicateM (n-1) $ (\[a,b]->(a,b)).map read.words <$> getLine
  let
    avec = V.fromList as
    tree = mkUGraph [1..n] edges :: Gr () ()
  putStr $ unwords $ map show $ solve n tree avec

inf = 1000000001
solve :: Int -> Gr () () -> Vector Int -> [Int]
solve n tree avec = filter inner [1..n]
  where
  inner node = go 0 node == inf
  go visited node
    | lose = a
    | otherwise = inf
    where
    a = V.unsafeIndex avec (node-1)
    lose = foldl' f True childs
    f acc child
      | child == visited = acc
      | otherwise = acc && a <= go node child
    childs = neighbors tree node