{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns, BinaryLiterals, CPP, DerivingStrategies  #-}
{-# LANGUAGE DerivingVia, FlexibleContexts, FlexibleInstances       #-}
{-# LANGUAGE GeneralizedNewtypeDeriving, KindSignatures, LambdaCase #-}
{-# LANGUAGE MagicHash, MultiParamTypeClasses, MultiWayIf           #-}
{-# LANGUAGE NumericUnderscores, OverloadedStrings, PatternSynonyms #-}
{-# LANGUAGE RankNTypes, RecordWildCards, ScopedTypeVariables       #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeApplications    #-}
{-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns  #-}
import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bool
import qualified Data.ByteString             as B
import qualified Data.ByteString.Builder     as B
import qualified Data.ByteString.Char8       as C
import qualified Data.ByteString.Internal    as B
import qualified Data.ByteString.Unsafe      as B
import           Data.Char
import qualified Data.Foldable               as F
import           Data.Function
import           Data.Functor.Identity
import qualified Data.IntMap.Strict          as IM
import qualified Data.IntSet                 as IS
import qualified Data.List                   as L
import qualified Data.Map.Strict             as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive
import           Data.Ratio
import           Data.Semigroup
import qualified Data.Set                    as S
import           Data.Tuple
import qualified Data.Vector                 as V
import qualified Data.Vector.Generic         as G
import qualified Data.Vector.Generic.Mutable as GM
import qualified Data.Vector.Mutable         as VM
import qualified Data.Vector.Unboxed         as U
import qualified Data.Vector.Unboxed.Mutable as UM
import           Debug.Trace
import           Foreign                     hiding (void)
import           GHC.Exts
import qualified System.IO                   as IO
import           Unsafe.Coerce


#define MOD 1000000007
#define FACT_CACHE_SIZE 200200

main :: IO ()
main = do
    n <- readLn
    es <- U.unfoldrN (n-1) (runParser $ (,) <$> int1 <*> int1) <$> C.getContents
    putStr.unlines.map show.U.toList $ solve n es

solve :: Int -> U.Vector (Int, Int) -> U.Vector IntMod
solve n es = U.map snd $ rerootingDP gr toM fold
  where
    !gr = buildUndirectedGraph n es

    toM :: (Int, IntMod) -> (Sum Int, Product IntMod)
    toM (sz, res) = coerce (sz, recipFact sz * res)

    fold :: Vertex -> (Sum Int, Product IntMod) -> (Int, IntMod)
    fold _ (Sum sz, Product res) = (sz + 1, fact sz * res)

rerootingDP
    :: forall w a m . (U.Unbox w, U.Unbox a, U.Unbox m, Monoid m)
    => SparseGraph w -> (a -> m) -> (Vertex -> m -> a) -> U.Vector a
rerootingDP gr toM foldChildren = dp2
  where
    root :: Vertex
    root = 0

    dp1 :: U.Vector a
    !dp1 = U.create $ do
        dp <- UM.unsafeNew (numVerticesCSR gr)
        fix (\dfs p v -> do
            res <- foldChildren v . U.foldl' (<>) mempty .  U.map toM
                <$> U.mapM (dfs v) (U.filter (/=p) $ gr `adj` v)
            UM.write dp v res
            return res
            ) (-1) root
        return dp

    dp2 :: U.Vector a
    dp2 = U.create $ do
        dp <- UM.unsafeNew (numVerticesCSR gr)
        UM.write dp root (dp1 U.! root)
        fix (\dfs parent !fromParent v ->  do
            let children = U.filter (/= parent) $ gr `adj` v
            UM.write dp v
                . foldChildren v . U.foldl' (<>) fromParent . U.map toM
                $ U.backpermute dp1 children
            let cumL = U.prescanl' (<>) mempty . U.map toM
                    $ U.backpermute dp1 children
            let cumR = U.prescanr' (<>) mempty . U.map toM
                    $ U.backpermute dp1 children
            U.zipWithM_ (dfs v . toM . foldChildren v . (<> fromParent))
                (U.zipWith (<>) cumL cumR) children
            ) (-1) mempty root
        return dp

-------------------------------------------------------------------------------
-- Utils
-------------------------------------------------------------------------------
rep :: Monad m => Int -> (Int -> m ()) -> m ()
rep !n = U.forM_ $ U.generate n id
{-# INLINE rep #-}
rev :: Monad m => Int -> (Int -> m ()) -> m ()
rev !n = U.forM_ $ U.iterateN n (subtract 1) (n - 1)
{-# INLINE rev #-}
infixl 8 `shiftRL`, `unsafeShiftRL`
shiftRL = unsafeShiftRL
{-# INLINE shiftRL #-}
unsafeShiftRL (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE unsafeShiftRL #-}
type Parser a = StateT C.ByteString Maybe a
runParser :: Parser a -> C.ByteString -> Maybe (a, C.ByteString)
runParser = runStateT
{-# INLINE runParser #-}
int :: Parser Int
int = coerce $ C.readInt . C.dropWhile isSpace
{-# INLINE int #-}
int1 :: Parser Int
int1 = fmap (subtract 1) int
{-# INLINE int1 #-}
char :: Parser Char
char = coerce C.uncons
{-# INLINE char #-}
byte :: Parser Word8
byte = coerce B.uncons
{-# INLINE byte #-}
-------------------------------------------------------------------------------
-- Data.VecQueue
-------------------------------------------------------------------------------
data VecQueue s a = VecQueue{intVarsVQ :: !(UM.MVector s Int), internalVecQueue :: !(UM.MVector s a)}
_dequeueCount :: Int
_dequeueCount = 0
{-# INLINE _dequeueCount #-}
_enqueueCount :: Int
_enqueueCount = 1
{-# INLINE _enqueueCount #-}
newVecQueue :: (PrimMonad m, UM.Unbox a) => Int -> m (VecQueue (PrimState m) a)
newVecQueue n = VecQueue <$> UM.replicate 2 0 <*> UM.unsafeNew n
defaultVecQueueSize :: Int
defaultVecQueueSize = 1024 * 1024
lengthVQ :: (PrimMonad m, UM.Unbox a) => VecQueue (PrimState m) a -> m Int
lengthVQ (VecQueue info _) = (-) <$> UM.unsafeRead info _enqueueCount <*> UM.unsafeRead info _dequeueCount
{-# INLINE lengthVQ #-}
dequeueVQ :: (PrimMonad m, UM.Unbox a) => VecQueue (PrimState m) a -> m (Maybe a)
dequeueVQ (VecQueue info q) = do { f <- UM.unsafeRead info _dequeueCount; r <- UM.unsafeRead info _enqueueCount; if f < r then do { UM.unsafeWrite info _dequeueCount (f + 1); pure <$> UM.unsafeRead q f} else return Nothing}
{-# INLINE dequeueVQ #-}
enqueueVQ :: (PrimMonad m, UM.Unbox a) => a -> VecQueue (PrimState m) a -> m ()
enqueueVQ x (VecQueue info q) = do { r <- UM.unsafeRead info _enqueueCount; UM.unsafeWrite q r x; UM.unsafeWrite info _enqueueCount (r + 1)}
{-# INLINE enqueueVQ #-}
enqueuesVQ :: (PrimMonad m, UM.Unbox a) => U.Vector a -> VecQueue (PrimState m) a -> m ()
enqueuesVQ vec (VecQueue info q) = do { r <- UM.unsafeRead info _enqueueCount; UM.unsafeWrite info _enqueueCount (r + U.length vec); U.unsafeCopy (UM.unsafeSlice r (U.length vec) q) vec}
{-# INLINE enqueuesVQ #-}
clearVQ :: (UM.Unbox a, PrimMonad m) => VecQueue (PrimState m) a -> m ()
clearVQ (VecQueue info _) = do { UM.unsafeWrite info _dequeueCount 0; UM.unsafeWrite info _enqueueCount 0}
freezeVecQueue :: (PrimMonad m, UM.Unbox a) => VecQueue (PrimState m) a -> m (U.Vector a)
freezeVecQueue (VecQueue info q) = do { f <- UM.unsafeRead info _dequeueCount; r <- UM.unsafeRead info _enqueueCount; U.unsafeFreeze $ UM.unsafeSlice f (r - f) q}
-------------------------------------------------------------------------------
-- Data.Graph.Sparse
-------------------------------------------------------------------------------
type Vertex = Int
type Edge = (Vertex, Vertex)
type EdgeWith w = (Vertex, Vertex, w)
type EdgeId = Int
data SparseGraph w = CSR{numVerticesCSR :: !Int, numEdgesCSR :: !Int, offsetCSR :: !(U.Vector Int), adjacentCSR :: !(U.Vector Vertex), edgeCtxCSR :: !(U.Vector w)}
data SparseGraphBuilder s w = SparseGraphBuilder{numVerticesSGB :: !Int, queueSGB :: VecQueue s (EdgeWith w), outDegSGB :: UM.MVector s Int}
buildSparseGraph :: (U.Unbox w) => Int -> (forall s . SparseGraphBuilder s w -> ST s ()) -> SparseGraph w
buildSparseGraph numVerticesCSR run = runST $ do { queueSGB <- newVecQueue (1024 * 1024); outDegSGB <- UM.replicate numVerticesCSR 0; run SparseGraphBuilder{numVerticesSGB = numVerticesCSR, ..}; numEdgesCSR <- lengthVQ queueSGB; offsetCSR <- U.scanl' (+) 0 <$> U.unsafeFreeze outDegSGB; moffset <- U.thaw offsetCSR; madj <- UM.unsafeNew numEdgesCSR; mectx <- UM.unsafeNew numEdgesCSR; edges <- freezeVecQueue queueSGB; U.forM_ edges $ \ (src, dst, w) -> do { pos <- UM.unsafeRead moffset src; UM.unsafeWrite moffset src (pos + 1); UM.unsafeWrite madj pos dst; UM.unsafeWrite mectx pos w}; adjacentCSR <- U.unsafeFreeze madj; edgeCtxCSR <- U.unsafeFreeze mectx; return CSR{..}}
{-# INLINE buildSparseGraph #-}
addDirectedEdge :: (U.Unbox w, PrimMonad m) => SparseGraphBuilder (PrimState m) w -> EdgeWith w -> m ()
addDirectedEdge SparseGraphBuilder{..} (src, dst, w) = do { enqueueVQ (src, dst, w) queueSGB; UM.unsafeModify outDegSGB (+ 1) src}
{-# INLINE addDirectedEdge #-}
addUndirectedEdge :: (U.Unbox w, PrimMonad m) => SparseGraphBuilder (PrimState m) w -> EdgeWith w -> m ()
addUndirectedEdge SparseGraphBuilder{..} (src, dst, w) = do { enqueueVQ (src, dst, w) queueSGB; enqueueVQ (dst, src, w) queueSGB; UM.unsafeModify outDegSGB (+ 1) src; UM.unsafeModify outDegSGB (+ 1) dst}
{-# INLINE addUndirectedEdge #-}
addDirectedEdge_ :: (PrimMonad m) => SparseGraphBuilder (PrimState m) () -> Edge -> m ()
addDirectedEdge_ SparseGraphBuilder{..} (src, dst) = do { enqueueVQ (src, dst, ()) queueSGB; UM.unsafeModify outDegSGB (+ 1) src}
{-# INLINE addDirectedEdge_ #-}
addUndirectedEdge_ :: (PrimMonad m) => SparseGraphBuilder (PrimState m) () -> Edge -> m ()
addUndirectedEdge_ SparseGraphBuilder{..} (src, dst) = do { enqueueVQ (src, dst, ()) queueSGB; enqueueVQ (dst, src, ()) queueSGB; UM.unsafeModify outDegSGB (+ 1) src; UM.unsafeModify outDegSGB (+ 1) dst}
{-# INLINE addUndirectedEdge_ #-}
buildDirectedGraph :: Int -> U.Vector Edge -> SparseGraph ()
buildDirectedGraph numVerticesCSR edges = buildSparseGraph numVerticesCSR $ \ builder -> do { U.mapM_ (addDirectedEdge_ builder) edges}
buildUndirectedGraph :: Int -> U.Vector Edge -> SparseGraph ()
buildUndirectedGraph numVerticesCSR edges = buildSparseGraph numVerticesCSR $ \ builder -> do { U.mapM_ (addUndirectedEdge_ builder) edges}
buildDirectedGraphW :: (U.Unbox w) => Int -> U.Vector (EdgeWith w) -> SparseGraph w
buildDirectedGraphW numVerticesCSR edges = buildSparseGraph numVerticesCSR $ \ builder -> do { U.mapM_ (addDirectedEdge builder) edges}
buildUndirectedGraphW :: (U.Unbox w) => Int -> U.Vector (EdgeWith w) -> SparseGraph w
buildUndirectedGraphW numVerticesCSR edges = buildSparseGraph numVerticesCSR $ \ builder -> do { U.mapM_ (addUndirectedEdge builder) edges}
adj :: SparseGraph w -> Vertex -> U.Vector Vertex
adj CSR{..} v = U.unsafeSlice o (o' - o) adjacentCSR where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE adj #-}
iadj :: SparseGraph w -> Vertex -> U.Vector (EdgeId, Vertex)
iadj CSR{..} v = U.imap ((,) . (+ o)) $ U.unsafeSlice o (o' - o) adjacentCSR where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE iadj #-}
adjW :: (U.Unbox w) => SparseGraph w -> Vertex -> U.Vector (Vertex, w)
adjW CSR{..} v = U.zip (U.unsafeSlice o (o' - o) adjacentCSR) (U.unsafeSlice o (o' - o) edgeCtxCSR) where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE adjW #-}
iadjW :: (U.Unbox w) => SparseGraph w -> Vertex -> U.Vector (EdgeId, Vertex, w)
iadjW CSR{..} v = U.izipWith (\ i u w -> (i + o, u, w)) (U.unsafeSlice o (o' - o) adjacentCSR) (U.unsafeSlice o (o' - o) edgeCtxCSR) where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE iadjW #-}
outEdges :: SparseGraph w -> Vertex -> U.Vector EdgeId
outEdges CSR{..} v = U.generate (o' - o) (+ o) where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE outEdges #-}
outDegree :: SparseGraph w -> Vertex -> Int
outDegree CSR{..} v = U.unsafeIndex offsetCSR (v + 1) - U.unsafeIndex offsetCSR v
{-# INLINE outDegree #-}
outDegrees :: SparseGraph w -> U.Vector Int
outDegrees CSR{..} = U.zipWith (-) offsetCSR $ U.tail offsetCSR
{-# INLINE outDegrees #-}
-------------------------------------------------------------------------------
-- Math.Combinatrics
-------------------------------------------------------------------------------
fact :: Int -> IntMod
fact = U.unsafeIndex factCache
{-# INLINE fact #-}
recipFact :: Int -> IntMod
recipFact = U.unsafeIndex recipFactCache
{-# INLINE recipFact #-}
perm :: Int -> Int -> IntMod
perm n k = fact n * recipFact k
{-# INLINE perm #-}
comb :: Int -> Int -> IntMod
comb n k = fact n * recipFact (n - k) * recipFact k
{-# INLINE comb #-}
factCacheSize :: Int
factCacheSize = min (modulus - 1) FACT_CACHE_SIZE
{-# INLINE factCacheSize #-}
factCache :: U.Vector IntMod
factCache = U.scanl' (\ x y -> x * coerce y) (1 :: IntMod) $ U.generate factCacheSize (+ 1)
{-# NOINLINE factCache #-}
recipFactCache :: U.Vector IntMod
recipFactCache = U.scanr' ((*) . coerce) (1 / factCache U.! factCacheSize) $ U.generate factCacheSize (+ 1)
{-# NOINLINE recipFactCache #-}
-------------------------------------------------------------------------------
-- Data.IntMod
-------------------------------------------------------------------------------
modulus :: (Num a) => a
modulus = MOD
{-# INLINE modulus #-}
infixr 8 ^%
infixl 7 *%, /%
infixl 6 +%, -%
(+%) :: Int -> Int -> Int
(I# x#) +% (I# y#) = case x# +# y# of { r# -> I# (r# -# ((r# >=# MOD#) *# MOD#))}
{-# INLINE (+%) #-}
(-%) :: Int -> Int -> Int
(I# x#) -% (I# y#) = case x# -# y# of { r# -> I# (r# +# ((r# <# 0#) *# MOD#))}
{-# INLINE (-%) #-}
(*%) :: Int -> Int -> Int
(I# x#) *% (I# y#) = I# ((x# *# y#) `remInt#` MOD#)
{-# INLINE (*%) #-}
(/%) :: Int -> Int -> Int
(I# x#) /% (I# y#) = go# y# MOD# 1# 0# where { go# a# b# u# v# | isTrue# (b# ># 0#) = case a# `quotInt#` b# of { q# -> go# b# (a# -# (q# *# b#)) v# (u# -# (q# *# v#))} | otherwise = I# ((x# *# (u# +# MOD#)) `remInt#` MOD#)}
{-# INLINE (/%) #-}
(^%) :: Int -> Int -> Int
x ^% n | n > 0 = go 1 x n | n == 0 = 1 | otherwise = go 1 (1 /% x) (-n) where { go !acc !y !m | m .&. 1 == 0 = go acc (y *% y) (unsafeShiftR m 1) | m == 1 = acc *% y | otherwise = go (acc *% y) (y *% y) (unsafeShiftR (m - 1) 1)}
newtype IntMod = IntMod{getIntMod :: Int} deriving newtype (Eq, Ord, Read, Show, Real, Prim)
intMod :: (Integral a) => a -> IntMod
intMod x = fromIntegral $ mod (fromIntegral x) MOD
{-# INLINE intMod #-}
intModValidate :: IntMod -> Bool
intModValidate (IntMod x) = 0 <= x && x < MOD
{-# INLINE intModValidate #-}
instance Bounded IntMod where { minBound = IntMod 0; maxBound = IntMod $ modulus - 1}
instance Enum IntMod where { toEnum = intMod; fromEnum = coerce}
instance Integral IntMod where { quotRem x y = (x / y, x - x / y * y); toInteger = coerce (toInteger @Int)}
instance Num IntMod where { (+) = coerce (+%); (-) = coerce (-%); (*) = coerce (*%); abs = id; signum = const (IntMod 1); fromInteger x = coerce @Int @IntMod . fromInteger $ mod x modulus}
instance Fractional IntMod where { (/) = coerce (/%); fromRational q = fromInteger (numerator q) / fromInteger (denominator q)}
newtype instance  UM.MVector s IntMod = MV_IntMod (UM.MVector s Int)
newtype instance  U.Vector IntMod = V_IntMod (U.Vector Int)
instance U.Unbox IntMod
instance GM.MVector UM.MVector IntMod where { basicLength (MV_IntMod v) = GM.basicLength v; {-# INLINE basicLength #-}; basicUnsafeSlice i n (MV_IntMod v) = MV_IntMod $ GM.basicUnsafeSlice i n v; {-# INLINE basicUnsafeSlice #-}; basicOverlaps (MV_IntMod v1) (MV_IntMod v2) = GM.basicOverlaps v1 v2; {-# INLINE basicOverlaps #-}; basicUnsafeNew n = MV_IntMod `liftM` GM.basicUnsafeNew n; {-# INLINE basicUnsafeNew #-}; basicInitialize (MV_IntMod v) = GM.basicInitialize v; {-# INLINE basicInitialize #-}; basicUnsafeReplicate n x = MV_IntMod `liftM` GM.basicUnsafeReplicate n (coerce x); {-# INLINE basicUnsafeReplicate #-}; basicUnsafeRead (MV_IntMod v) i = coerce `liftM` GM.basicUnsafeRead v i; {-# INLINE basicUnsafeRead #-}; basicUnsafeWrite (MV_IntMod v) i x = GM.basicUnsafeWrite v i (coerce x); {-# INLINE basicUnsafeWrite #-}; basicClear (MV_IntMod v) = GM.basicClear v; {-# INLINE basicClear #-}; basicSet (MV_IntMod v) x = GM.basicSet v (coerce x); {-# INLINE basicSet #-}; basicUnsafeCopy (MV_IntMod v1) (MV_IntMod v2) = GM.basicUnsafeCopy v1 v2; {-# INLINE basicUnsafeCopy #-}; basicUnsafeMove (MV_IntMod v1) (MV_IntMod v2) = GM.basicUnsafeMove v1 v2; {-# INLINE basicUnsafeMove #-}; basicUnsafeGrow (MV_IntMod v) n = MV_IntMod `liftM` GM.basicUnsafeGrow v n; {-# INLINE basicUnsafeGrow #-}}
instance G.Vector U.Vector IntMod where { basicUnsafeFreeze (MV_IntMod v) = V_IntMod `liftM` G.basicUnsafeFreeze v; {-# INLINE basicUnsafeFreeze #-}; basicUnsafeThaw (V_IntMod v) = MV_IntMod `liftM` G.basicUnsafeThaw v; {-# INLINE basicUnsafeThaw #-}; basicLength (V_IntMod v) = G.basicLength v; {-# INLINE basicLength #-}; basicUnsafeSlice i n (V_IntMod v) = V_IntMod $ G.basicUnsafeSlice i n v; {-# INLINE basicUnsafeSlice #-}; basicUnsafeIndexM (V_IntMod v) i = coerce `liftM` G.basicUnsafeIndexM v i; {-# INLINE basicUnsafeIndexM #-}; basicUnsafeCopy (MV_IntMod mv) (V_IntMod v) = G.basicUnsafeCopy mv v; elemseq _ = seq; {-# INLINE elemseq #-}}
