{-# LANGUAGE MultiWayIf #-}

module Main where

import           Control.Monad
import qualified Data.Array                    as A
import qualified Data.Array.IO                 as AIO
import qualified Data.Array.Unboxed            as AU
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.List
import qualified Data.Map.Strict               as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
import qualified Data.Vector                   as V
--import           Data.Vector.Algorithms.Search
import qualified Data.Vector.Mutable           as VM
import qualified Data.Vector.Unboxed           as VU
import qualified Data.Vector.Unboxed.Mutable   as VUM
import           Debug.Trace
import qualified Data.Heap                     as H
main = do
  [iN, iM] <- getIL
  iAB      <- replicateM iM getIT2Order

  let mAB = foldl
        (\acc x ->
          let lr = M.insertWith (++) (fst x) [snd x] acc
          in  M.insertWith (++) (snd x) [fst x] lr
        )
        M.empty
        iAB

  arrows <- VUM.replicate iN (iN + 1)
  hists  <- VUM.replicate iN False

  bfs mAB arrows hists [1]

  fArrows <- VU.freeze arrows
  putStrLn "Yes"
  VU.forM_ (VU.tail fArrows) print

type Graph = M.Map Int [Int]
bfs :: Graph -> VUM.IOVector Int -> VUM.IOVector Bool -> [Int] -> IO ()
bfs graphAB arrows hists targs = do
  nextTarg <- concat <$> forM
    targs
    (\targ ->
      foldM
        (\acc nextTarg -> do
          hist <- VUM.read hists (p nextTarg)
          if not hist
            then do
              VUM.write hists (p nextTarg) True
              VUM.write arrows (p nextTarg) targ
              return (nextTarg : acc)
            else return acc
        )
        ([] :: [Int])
        (getListFromGraph targ) :: IO [Int]
    )
  when (nextTarg /= []) $ bfs graphAB arrows hists nextTarg
 where
  getListFromGraph :: Int -> [Int]
  getListFromGraph x = fromJustList $graphAB M.!? x

p :: Int -> Int
p x = x - 1

getIT2Order :: IO (Int, Int)
getIT2Order =
  getIL >>= \x@[xz, xo] -> if xz > xo then return (xo, xz) else return (xz, xo)

fromJustList :: Maybe [a] -> [a]
fromJustList (Just x) = x
fromJustList Nothing  = []

fromJustInt :: Maybe Int -> Int
fromJustInt (Just x) = x
fromJustInt Nothing  = 0

getVUI :: IO (VU.Vector Int)
getVUI = VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine

getRepVUI :: Int -> IO (VU.Vector Int)
getRepVUI n =
  VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace)
    .   BSC8.unlines
    <$> replicateM n BSC8.getLine

getVS :: IO (V.Vector Char)
getVS = V.fromList <$> getLine

getVUS :: IO (VU.Vector Char)
getVUS = VU.fromList <$> getLine

readI :: BSC8.ByteString -> Int
readI = fst . fromJust . BSC8.readInt

readIL :: BSC8.ByteString -> [Int]
readIL = map readI . BSC8.words

readIT2 :: BSC8.ByteString -> (Int, Int)
readIT2 bs =
  let words = BSC8.words bs in (readI $ head words, readI $ last words)

getI :: IO Int
getI = readI <$> BSC8.getLine

getIL :: IO [Int]
getIL = readIL <$> BSC8.getLine

get2IT :: IO (Int, Int)
get2IT = readIT2 <$> BSC8.getLine

getNIS :: Int -> IO [(Int, BSC8.ByteString)]
getNIS 0 = return []
getNIS n = do
  [aFst, aSnd] <- BSC8.words <$> BSC8.getLine
  next         <- getNIS (n - 1)
  return ((readI aFst, aSnd) : next)

il2ss :: [Int] -> String
il2ss = unwords . map show

il2sn :: [Int] -> String
il2sn = unlines . map show

--modNum = 10 ^ 9 + 7
modulus = 1000000007

newtype MInt = M Int

instance Num MInt where
  (M a) + (M b) = M $ mod (a + b) modulus

  (M a) - (M b) = M (a - b)

  (M a) * (M b) = M $ mod (a * b) modulus

  fromInteger a = M $ mod (fromInteger a) modulus

  abs (M a) = M $ abs a

  signum (M a) = M $ signum a

instance Show MInt where
  show (M a) = show (mod a modulus)

int2MInt :: Int -> MInt
int2MInt a = M (mod a modulus)

mInt2Int :: MInt -> Int
mInt2Int (M a) = a

factsMod :: V.Vector MInt
factsMod = V.scanl (\acc x -> M x * acc) 1 $ V.generate 200000 (+ 1)

factMod :: Int -> MInt
factMod = (factsMod V.!)

powMod :: MInt -> Int -> MInt
powMod n k = n ^ k

invMod :: MInt -> MInt
invMod (M 0) = error "inverse of 0"
invMod x     = powMod x (modulus - 2)

combMod :: Int -> Int -> MInt
combMod n k
  | n < 0 || k < 0 || k > n = 0
  | otherwise = factMod n * invMod (factMod (n - k)) * invMod (factMod k)

comb :: Int -> Int -> Int
comb n k | n < 0 || k < 0 || k > n = 0
         | k == n                  = 1
         | otherwise               = div (div (fact n) (fact (n - k))) (fact k)

primes :: V.Vector MInt
primes = V.scanl (\acc x -> M x * acc) 1 $ V.generate 200000 (+ 1)

fact :: Int -> Int
fact 0         = 1
fact n | n > 0 = n * fact (n - 1)

knappsackMaxVal
  :: AIO.IOArray (Int, Int) Int
  -> VU.Vector Int
  -> VU.Vector Int
  -> Int
  -> IO Int
knappsackMaxVal dp volumeVec valueVec dpSize = do
  mapM_
    (\i -> mapM_
      (\v -> do
        let volume = volumeVec VU.! i
            value  = valueVec VU.! i
        newdp <- if v < volume
          then AIO.readArray dp (i, v)
          else do
            dpIVm <- AIO.readArray dp (i, v - volume)
            dpIV  <- AIO.readArray dp (i, v)
            return (max (dpIVm + value) dpIV)
        AIO.writeArray dp (i + 1, v) newdp
      )
      [0 .. dpSize]
    )
    [0 .. VU.length volumeVec - 1]
  AIO.readArray dp (VU.length volumeVec, dpSize)

knappsackMinVol
  :: AIO.IOArray (Int, Int) Int
  -> VU.Vector Int
  -> VU.Vector Int
  -> Int
  -> Int
  -> IO Int
knappsackMinVol dp volumeVec valueVec dpSize maxVolume = do
  mapM_
    (\i -> mapM_
      (\v -> do
        let volume = volumeVec VU.! i
            value  = valueVec VU.! i
        newdp <- if (v + value) > dpSize
          then AIO.readArray dp (i, v)
          else do
            dpIVm <- AIO.readArray dp (i, v + value)
            dpIV  <- AIO.readArray dp (i, v)
            return (min (dpIVm - volume) dpIV)
        AIO.writeArray dp (i + 1, v) newdp
      )
      (reverse [0 .. dpSize])
    )
    [0 .. VU.length valueVec - 1]
  foldM
    (\acc x -> do
      num <- AIO.readArray dp (VU.length volumeVec, x)
      return $ if num <= maxVolume then x else acc
    )
    0
    [0 .. dpSize]

hMaxPoint :: Int
hMaxPoint = 100
hMaximum :: H.Heap Int -> Int
hMaximum h = hMaxPoint - (H.minimum h)
hInsertMax :: Int -> H.Heap Int -> H.Heap Int
hInsertMax x = H.insert (hMaxPoint - x)
hDeleteMax :: H.Heap Int -> H.Heap Int
hDeleteMax = H.deleteMin

myFilter :: (a -> Bool) -> [a] -> ([a], [a])
myFilter _pred [] = ([], [])
myFilter pred (x : xs)
  | pred x    = let (l, r) = myFilter pred xs in (x : l, r)
  | otherwise = let (l, r) = myFilter pred xs in (l, x : r)


Measured memory_bytes: 90064