Problem:
Score : 600 points

Problem Statement

We have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i.
For each k=1, ..., N, solve the problem below:

Consider writing a number on each vertex in the tree in the following manner:

First, write 1 on Vertex k.

Then, for each of the numbers 2, ..., N in this order, write the number on the vertex chosen as follows:

Choose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.

Find the number of ways in which we can write the numbers on the vertices, modulo (10^9+7).

Constraints

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

1 \leq a_i,b_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}

Output

For each k=1, 2, ..., N in this order, print a line containing the answer to the problem.

Sample Input 1

3
1 2
1 3

Sample Output 1

2
1
1

The graph in this input is as follows:

For k=1, there are two ways in which we can write the numbers on the vertices, as follows:

Writing 1, 2, 3 on Vertex 1, 2, 3, respectively

Writing 1, 3, 2 on Vertex 1, 2, 3, respectively

Sample Input 2

2
1 2

Sample Output 2

1
1

The graph in this input is as follows:

Sample Input 3

5
1 2
2 3
3 4
3 5

Sample Output 3

2
8
12
3
3

The graph in this input is as follows:

Sample Input 4

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

Sample Output 4

40
280
840
120
120
504
72
72

The graph in this input is as follows:

Solution in Go (1.14.1) (judge verdict: Accepted)

/*
URL:
https://atcoder.jp/contests/abc160/tasks/abc160_f
*/

package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"math"
	"os"
	"strconv"
)

/********** FAU standard libraries **********/

//fmt.Sprintf("%b\n", 255) 	// binary expression

/********** I/O usage **********/

//str := ReadString()
//i := ReadInt()
//X := ReadIntSlice(n)
//S := ReadRuneSlice()
//a := ReadFloat64()
//A := ReadFloat64Slice(n)

//str := ZeroPaddingRuneSlice(num, 32)
//str := PrintIntsLine(X...)

/*******************************************************************/

const (
	// General purpose
	MOD = 1000000000 + 7
	// MOD          = 998244353
	ALPHABET_NUM = 26
	INF_INT64    = math.MaxInt64
	INF_BIT60    = 1 << 60
	INF_INT32    = math.MaxInt32
	INF_BIT30    = 1 << 30
	NIL          = -1

	// for dijkstra, prim, and so on
	WHITE = 0
	GRAY  = 1
	BLACK = 2
)

func init() {
	// bufio.ScanWords <---> bufio.ScanLines
	ReadString = newReadString(os.Stdin, bufio.ScanWords)
	stdout = bufio.NewWriter(os.Stdout)
}

var (
	n     int
	edges [][]int
)

func main() {
	n = ReadInt()
	for i := 0; i < n-1; i++ {
		a, b := ReadInt2()
		a--
		b--

		e := []int{a, b}
		edges = append(edges, e)
	}

	cf := NewCombFactorial(500000)
	f := func(l, r T) T {
		total := int(l.size + r.size)
		res := cf.C(total, l.size)
		res = CalcMod(res*l.num, MOD)
		res = CalcMod(res*r.num, MOD)

		return T{size: total, num: res}
	}
	g := func(t T, idx int) T {
		return T{size: t.size + 1, num: t.num}
	}
	ti := T{size: 0, num: 1}
	// s := NewReRooting(n, G[:n], ti, f, g)
	s := NewReRootingSolver(n, edges, ti, f, g)
	for i := 0; i < n; i++ {
		fmt.Println(s.Query(i).num)
	}
}

// CalcMod can calculate a right residual whether value is positive or negative.
func CalcMod(val, m int) int {
	res := val % m
	if res < 0 {
		res += m
	}
	return res
}

// type T int
type T struct {
	size, num int
}

type ReRootingSolver struct {
	NodeCount int

	Adjacents         [][]int
	IndexForAdjacents [][]int

	Res []T
	DP  [][]T

	Identity    T
	Operate     func(l, r T) T
	OperateNode func(v T, p int) T
}

func NewReRootingSolver(
	nodeCount int, edges [][]int, identity T, operate func(l, r T) T, operateNode func(v T, p int) T,
) *ReRootingSolver {
	s := new(ReRootingSolver)

	s.NodeCount = nodeCount
	s.Identity = identity
	s.Operate = operate
	s.OperateNode = operateNode

	s.Adjacents = make([][]int, nodeCount)
	s.IndexForAdjacents = make([][]int, nodeCount)
	for _, e := range edges {
		s.IndexForAdjacents[e[0]] = append(s.IndexForAdjacents[e[0]], len(s.Adjacents[e[1]]))
		s.IndexForAdjacents[e[1]] = append(s.IndexForAdjacents[e[1]], len(s.Adjacents[e[0]]))
		s.Adjacents[e[0]] = append(s.Adjacents[e[0]], e[1])
		s.Adjacents[e[1]] = append(s.Adjacents[e[1]], e[0])
	}

	s.DP = make([][]T, len(s.Adjacents))
	s.Res = make([]T, len(s.Adjacents))

	for i := 0; i < len(s.Adjacents); i++ {
		s.DP[i] = make([]T, len(s.Adjacents[i]))
	}

	if s.NodeCount > 1 {
		s.Initialize()
	} else {
		s.Res[0] = s.OperateNode(s.Identity, 0)
	}

	return s
}

func (s *ReRootingSolver) Query(node int) T {
	return s.Res[node]
}

func (s *ReRootingSolver) Initialize() {
	parents, order := make([]int, s.NodeCount), make([]int, s.NodeCount)

	// InitOrderedTree
	index := 0
	stack := []int{}
	stack = append(stack, 0)
	parents[0] = -1
	for len(stack) > 0 {
		node := stack[len(stack)-1]
		stack = stack[:len(stack)-1]
		order[index] = node
		index++
		for i := 0; i < len(s.Adjacents[node]); i++ {
			adjacent := s.Adjacents[node][i]
			if adjacent == parents[node] {
				continue
			}
			stack = append(stack, adjacent)
			parents[adjacent] = node
		}
	}

	// fromLeaf
	for i := len(order) - 1; i >= 1; i-- {
		node := order[i]
		parent := parents[node]

		accum := s.Identity
		parentIndex := -1
		for j := 0; j < len(s.Adjacents[node]); j++ {
			if s.Adjacents[node][j] == parent {
				parentIndex = j
				continue
			}
			accum = s.Operate(accum, s.DP[node][j])
		}
		s.DP[parent][s.IndexForAdjacents[node][parentIndex]] = s.OperateNode(accum, node)
	}

	// toLeaf
	for i := 0; i < len(order); i++ {
		node := order[i]
		accum := s.Identity
		accumsFromTail := make([]T, len(s.Adjacents[node]))
		accumsFromTail[len(accumsFromTail)-1] = s.Identity
		for j := len(accumsFromTail) - 1; j >= 1; j-- {
			accumsFromTail[j-1] = s.Operate(s.DP[node][j], accumsFromTail[j])
		}
		for j := 0; j < len(accumsFromTail); j++ {
			s.DP[s.Adjacents[node][j]][s.IndexForAdjacents[node][j]] = s.OperateNode(s.Operate(accum, accumsFromTail[j]), node)
			accum = s.Operate(accum, s.DP[node][j])
		}
		s.Res[node] = s.OperateNode(accum, node)
	}
}

// cf := NewCombFactorial(2000000) // maxNum == "maximum n" * 2 (for H(n,r))
// res := cf.C(n, r) 	// 組み合わせ
// res := cf.H(n, r) 	// 重複組合せ
// res := cf.P(n, r) 	// 順列

type CombFactorial struct {
	factorial, invFactorial []int
	maxNum                  int
}

func NewCombFactorial(maxNum int) *CombFactorial {
	cf := new(CombFactorial)
	cf.maxNum = maxNum
	cf.factorial = make([]int, maxNum+50)
	cf.invFactorial = make([]int, maxNum+50)
	cf.initCF()

	return cf
}
func (c *CombFactorial) modInv(a int) int {
	return c.modpow(a, MOD-2)
}
func (c *CombFactorial) modpow(a, e int) int {
	if e == 0 {
		return 1
	}

	if e%2 == 0 {
		halfE := e / 2
		half := c.modpow(a, halfE)
		return half * half % MOD
	}

	return a * c.modpow(a, e-1) % MOD
}
func (c *CombFactorial) initCF() {
	var i int

	for i = 0; i <= c.maxNum; i++ {
		if i == 0 {
			c.factorial[i] = 1
			c.invFactorial[i] = c.modInv(c.factorial[i])
			continue
		}

		num := i * c.factorial[i-1]
		num %= MOD
		c.factorial[i] = num
		c.invFactorial[i] = c.modInv(c.factorial[i])
	}
}
func (c *CombFactorial) C(n, r int) int {
	var res int

	res = 1
	res *= c.factorial[n]
	res %= MOD
	res *= c.invFactorial[r]
	res %= MOD
	res *= c.invFactorial[n-r]
	res %= MOD

	return res
}
func (c *CombFactorial) P(n, r int) int {
	var res int

	res = 1
	res *= c.factorial[n]
	res %= MOD
	res *= c.invFactorial[n-r]
	res %= MOD

	return res
}
func (c *CombFactorial) H(n, r int) int {
	return c.C(n-1+r, r)
}

/*******************************************************************/

/*********** I/O ***********/

var (
	// ReadString returns a WORD string.
	ReadString func() string
	stdout     *bufio.Writer
)

func newReadString(ior io.Reader, sf bufio.SplitFunc) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+9)) // for Codeforces
	r.Split(sf)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

// ReadInt returns an integer.
func ReadInt() int {
	return int(readInt64())
}
func ReadInt2() (int, int) {
	return int(readInt64()), int(readInt64())
}
func ReadInt3() (int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64())
}
func ReadInt4() (int, int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64()), int(readInt64())
}

// ReadInt64 returns as integer as int64.
func ReadInt64() int64 {
	return readInt64()
}
func ReadInt64_2() (int64, int64) {
	return readInt64(), readInt64()
}
func ReadInt64_3() (int64, int64, int64) {
	return readInt64(), readInt64(), readInt64()
}
func ReadInt64_4() (int64, int64, int64, int64) {
	return readInt64(), readInt64(), readInt64(), readInt64()
}

func readInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// ReadIntSlice returns an integer slice that has n integers.
func ReadIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt()
	}
	return b
}

// ReadInt64Slice returns as int64 slice that has n integers.
func ReadInt64Slice(n int) []int64 {
	b := make([]int64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt64()
	}
	return b
}

// ReadFloat64 returns an float64.
func ReadFloat64() float64 {
	return float64(readFloat64())
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(ReadString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// ReadFloatSlice returns an float64 slice that has n float64.
func ReadFloat64Slice(n int) []float64 {
	b := make([]float64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadFloat64()
	}
	return b
}

// ReadRuneSlice returns a rune slice.
func ReadRuneSlice() []rune {
	return []rune(ReadString())
}

/*********** Debugging ***********/

// ZeroPaddingRuneSlice returns binary expressions of integer n with zero padding.
// For debugging use.
func ZeroPaddingRuneSlice(n, digitsNum int) []rune {
	sn := fmt.Sprintf("%b", n)

	residualLength := digitsNum - len(sn)
	if residualLength <= 0 {
		return []rune(sn)
	}

	zeros := make([]rune, residualLength)
	for i := 0; i < len(zeros); i++ {
		zeros[i] = '0'
	}

	res := []rune{}
	res = append(res, zeros...)
	res = append(res, []rune(sn)...)

	return res
}

// Strtoi is a wrapper of strconv.Atoi().
// If strconv.Atoi() returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// PrintIntsLine returns integers string delimited by a space.
func PrintIntsLine(A ...int) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.Itoa(A[i])
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintIntsLine returns integers string delimited by a space.
func PrintInts64Line(A ...int64) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.FormatInt(A[i], 10) // 64bit int version
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintfDebug is wrapper of fmt.Fprintf(os.Stderr, format, a...)
func PrintfDebug(format string, a ...interface{}) {
	fmt.Fprintf(os.Stderr, format, a...)
}

// PrintfBufStdout is function for output strings to buffered os.Stdout.
// You may have to call stdout.Flush() finally.
func PrintfBufStdout(format string, a ...interface{}) {
	fmt.Fprintf(stdout, format, a...)
}