Problem:
Score : 500 points

Problem Statement

You are given a connected undirected simple graph, which has N vertices and M edges.
The vertices are numbered 1 through N, and the edges are numbered 1 through M.
Edge i connects vertices A_i and B_i.
Your task is to find a path that satisfies the following conditions:

The path traverses two or more vertices.

The path does not traverse the same vertex more than once.

A vertex directly connected to at least one of the endpoints of the path, is always contained in the path.

It can be proved that such a path always exists.
Also, if there are more than one solution, any of them will be accepted.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i < B_i \leq N

The given graph is connected and simple (that is, for every pair of vertices, there is at most one edge that directly connects them).

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Find one path that satisfies the conditions, and print it in the following format.
In the first line, print the count of the vertices contained in the path.
In the second line, print a space-separated list of the indices of the vertices, in order of appearance in the path.

Sample Input 1

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

Sample Output 1

4
2 3 1 4

There are two vertices directly connected to vertex 2: vertices 3 and 4.
There are also two vertices directly connected to vertex 4: vertices 1 and 2.
Hence, the path 2 → 3 → 1 → 4 satisfies the conditions.

Sample Input 2

7 8
1 2
2 3
3 4
4 5
5 6
6 7
3 5
2 6

Sample Output 2

7
1 2 3 4 5 6 7

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

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UnboxedTuples #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE MultiWayIf #-}

import Control.Monad
import Control.Monad.ST
import Control.Monad.State
import Control.Monad.Primitive
import Control.Applicative
import Control.Arrow
import Data.List
import Data.Array
import Data.Array.IO
import Data.Array.ST
import Data.IORef
import Data.STRef
import Data.Maybe
import Data.Bits
import Data.Ord
import Data.Ratio
import Data.Int
import Data.Char
import qualified Data.ByteString.Char8 as BS
import qualified Data.Set as Set
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector.Generic as VG
import qualified Data.Vector.Generic.Mutable as VGM
import Data.Tuple
import Data.Function
import Text.Printf
import Debug.Trace
import Numeric

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

listToTuple2 [a,b] = (a,b)
listToTuple3 [a,b,c] = (a,b,c)
listToTuple4 [a,b,c,d] = (a,b,c,d)
listToTuple5 [a,b,c,d,e] = (a,b,c,d,e)

readIntBS = fst . fromJust . BS.readInt

for = flip map

infixr 1 ?
(?) :: Bool -> (a,a) -> a
(?) b t = (if b then fst else snd) t

main :: IO ()
main = do
  [n,m] <- map read . words <$> getLine :: IO [Int]
  graph <- buildWeightedUndirectedGraph (1,n) . map (listToTuple2 . map readIntBS . BS.words) . BS.lines <$> BS.getContents :: IO (Array Int [Int])
  
  check <- newArray (1,n) False :: IO (IOUArray Int Bool)

  let
    search cur = do
      writeArray check cur True
      
      let neighb = graph!cur
      next <- (filterM (\i -> not <$> readArray check i) neighb)
      

      if null next then
        return [cur]
        else
        (cur:) <$> search (head next)

  path <- (++) <$> (reverse <$> search 1) <*> (tail <$> search 1)
  print $ length path
  putStrLn $ unwords . map show $ path

type Node = Int

{-- 重みなし無向グラフ --}
buildWeightedUndirectedGraph :: (Node,Node) -> [(Node,Node)] -> Array Node [Node]
buildWeightedUndirectedGraph bound dat = runST $ do
  graph <- newArray bound [] :: ST s (STArray s Node [Node])
  forM_ dat $ \(s,e) -> do
    modifyArray graph s (e:)
    modifyArray graph e (s:)
  freeze graph