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:



Sample input:
3
1 2
1 3


Sample output:
2
1
1

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Fri May  8 12:10:59 2020

@author: ybt07
"""

import sys
sys.setrecursionlimit(3*10**5)  # 繰り返し制限

# 組み合わせ
N = 2*10**5   # 問題サイズに合わせて変えておく
MOD = 10**9 + 7

# modint
# https://qiita.com/wotsushi/items/c936838df992b706084c

class ModInt:
    def __init__(self, x):
        self.x = x % MOD

    def __str__(self):
        return str(self.x)

    __repr__ = __str__

    def __add__(self, other):
        return (
            ModInt(self.x + other.x) if isinstance(other, ModInt) else
            ModInt(self.x + other)
        )

    def __sub__(self, other):
        return (
            ModInt(self.x - other.x) if isinstance(other, ModInt) else
            ModInt(self.x - other)
        )

    def __mul__(self, other):
        return (
            ModInt(self.x * other.x) if isinstance(other, ModInt) else
            ModInt(self.x * other)
        )

    # / : 商。　逆元はフェルマーの小定理を利用している
    '''
    def __truediv__(self, other):
        return (
            ModInt(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(self.x * pow(other, MOD - 2, MOD))
        )
    '''

    def __truediv__(self, other):
        return (
            ModInt(
                self.x * inv[other.x]
            ) if isinstance(other, ModInt) else
            ModInt(self.x * inv[other])
        )


    # ** : 指数
    def __pow__(self, other):
        return (
            ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(self.x, other, MOD))
        )

    # x が Modint、y が通常の int の場合に、y.__add__(x) に対して、何を適用するか、定義している（→ x.__add__(y)を呼べ） 
    __radd__ = __add__

    def __rsub__(self, other):
        return (
            ModInt(other.x - self.x) if isinstance(other, ModInt) else
            ModInt(other - self.x)
        )

    __rmul__ = __mul__

    def __rtruediv__(self, other):
        return (
            ModInt(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(other * pow(self.x, MOD - 2, MOD))
        )

    def __rpow__(self, other):
        return (
            ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(other, self.x, MOD))
        )

def cmb(n, r):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return ModInt(fac[n] * facinv[r] * facinv[n-r])

fac = [1, 1] # 元テーブル
facinv = [1, 1] #逆元テーブル
inv = [0, 1] #逆元テーブル計算用テーブル

for i in range(2, N):
    fac.append( ( fac[-1] * i ) % MOD )
    inv.append( ( -inv[MOD % i] * (MOD//i) ) % MOD )
    facinv.append( (facinv[-1] * inv[-1]) % MOD )

# 部分木のDP値を求めていく
# u : 求める頂点
# 親（親側に辿らないように） p

def dfs(u, p = -1):

    global DP, CN, E
    
    tmp_ans = 1
    tmp_cn = 0  # （自分を含む）部分木のノード数

    # u から出ている頂点 v
    for v in E[u]:
        if v != p:  # 親への辺以外について
            DP[v], CN[v] = dfs(v, u)
            tmp_cn += CN[v]
            tmp_ans *= DP[v] * cmb(tmp_cn, CN[v])
    DP[u] = tmp_ans
    CN[u] = tmp_cn + 1
            
    return tmp_ans, tmp_cn + 1

# 各頂点の真のDP値を求めていく

def bfs(u, p=-1):
    
    global DP, E
    
    tmp_ans = DP[u]
    tmp_cn = 1
    
    for v in E[u]:  # 各vに対して「真のDP値」を求めていく
        if v == p:
            continue
            
        # DP[u] と DP[v] から DP[v <- u] を求める
        tmp_cn = N - CN[v]  # v から見たときの u の部分木の要素数
        # print(v+1,tmp_cn)
        # tmp_ans = DP[u] / DP[v] / cmb(N - 1, CN[v])
                
        # DP[u <- v] を使って、DP[v] を更新する
        # DP[v] = DP[v] * tmp_ans * cmb(N-1, tmp_cn)

        # print(v+1,tmp_cn)
        # tmp_ans = DP[u] / cmb(N - 1, CN[v])
                
        # DP[u <- v] を使って、DP[v] を更新する
        DP[v] = DP[u] * CN[v] / (N - CN[v]) 

        bfs(v, u)
    
    return

# 入力処理
N = int(input())  # 頂点数
E = [[] for _ in range(N)]  # 辺の情報

for _ in range(N - 1):
    a, b = map(int, input().split())
    E[a-1].append(b-1)  # 双方向の情報
    E[b-1].append(a-1)
    
DP = [ModInt(1)] * N
CN = [0] * N

dfs(0)
bfs(0)

for i in DP:
    print(i)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Fri May  8 12:10:59 2020

@author: ybt07
"""

import sys
sys.setrecursionlimit(3*10**5)  # 繰り返し制限

# 組み合わせ
N = 2*10**5   # 問題サイズに合わせて変えておく
MOD = 10**9 + 7

# modint
# https://qiita.com/wotsushi/items/c936838df992b706084c

class ModInt:
    def __init__(self, x):
        self.x = x % MOD

    def __str__(self):
        return str(self.x)

    __repr__ = __str__

    def __add__(self, other):
        return (
            ModInt(self.x + other.x) if isinstance(other, ModInt) else
            ModInt(self.x + other)
        )

    def __sub__(self, other):
        return (
            ModInt(self.x - other.x) if isinstance(other, ModInt) else
            ModInt(self.x - other)
        )

    def __mul__(self, other):
        return (
            ModInt(self.x * other.x) if isinstance(other, ModInt) else
            ModInt(self.x * other)
        )

    # / : 商。　逆元はフェルマーの小定理を利用している
    def __truediv__(self, other):
        return (
            ModInt(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(self.x * pow(other, MOD - 2, MOD))
        )

    # ** : 指数
    def __pow__(self, other):
        return (
            ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(self.x, other, MOD))
        )

    # x が Modint、y が通常の int の場合に、y.__add__(x) に対して、何を適用するか、定義している（→ x.__add__(y)を呼べ） 
    __radd__ = __add__

    def __rsub__(self, other):
        return (
            ModInt(other.x - self.x) if isinstance(other, ModInt) else
            ModInt(other - self.x)
        )

    __rmul__ = __mul__

    def __rtruediv__(self, other):
        return (
            ModInt(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(other * pow(self.x, MOD - 2, MOD))
        )

    def __rpow__(self, other):
        return (
            ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(other, self.x, MOD))
        )

def cmb(n, r):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return ModInt(fac[n] * facinv[r] * facinv[n-r])

fac = [1, 1] # 元テーブル
facinv = [1, 1] #逆元テーブル
inv = [0, 1] #逆元テーブル計算用テーブル

for i in range(2, N):
    fac.append( ( fac[-1] * i ) % MOD )
    inv.append( ( -inv[MOD % i] * (MOD//i) ) % MOD )
    facinv.append( (facinv[-1] * inv[-1]) % MOD )

# 部分木のDP値を求めていく
# u : 求める頂点
# 親（親側に辿らないように） p

def dfs(u, p = -1):

    global DP, CN, E
    
    tmp_ans = 1
    tmp_cn = 0  # （自分を含む）部分木のノード数

    # u から出ている頂点 v
    for v in E[u]:
        if v != p:  # 親への辺以外について
            DP[v], CN[v] = dfs(v, u)
            tmp_cn += CN[v]
            tmp_ans *= DP[v] * cmb(tmp_cn, CN[v])
    DP[u] = tmp_ans
    CN[u] = tmp_cn + 1
            
    return tmp_ans, tmp_cn + 1

# 各頂点の真のDP値を求めていく

def bfs(u, p=-1):
    
    global DP, E
    
    tmp_ans = DP[u]
    tmp_cn = 1
    
    for v in E[u]:  # 各vに対して「真のDP値」を求めていく
        if v == p:
            continue
            
        # DP[u] と DP[v] から DP[v <- u] を求める
        tmp_cn = N - CN[v]  # v から見たときの u の部分木の要素数
        # print(v+1,tmp_cn)
        tmp_ans = DP[u] / DP[v] / cmb(N - 1, CN[v])
                
        # DP[u <- v] を使って、DP[v] を更新する
        DP[v] = DP[v] * tmp_ans * cmb(N-1, tmp_cn)
        bfs(v, u)
    
    return

# 入力処理
N = int(input())  # 頂点数
E = [[] for _ in range(N)]  # 辺の情報

for _ in range(N - 1):
    a, b = map(int, input().split())
    E[a-1].append(b-1)  # 双方向の情報
    E[b-1].append(a-1)
    
DP = [ModInt(1)] * N
CN = [0] * N

dfs(0)
bfs(0)

for i in DP:
    print(i)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Fri May  8 12:10:59 2020

@author: ybt07
"""

import sys
sys.setrecursionlimit(3*10**5)  # 繰り返し制限

# 組み合わせ
N = 2*10**5   # 問題サイズに合わせて変えておく
MOD = 10**9 + 7

# modint
# https://qiita.com/wotsushi/items/c936838df992b706084c

class ModInt:
    def __init__(self, x):
        self.x = x % MOD

    def __str__(self):
        return str(self.x)

    __repr__ = __str__

    def __add__(self, other):
        return (
            ModInt(self.x + other.x) if isinstance(other, ModInt) else
            ModInt(self.x + other)
        )

    def __sub__(self, other):
        return (
            ModInt(self.x - other.x) if isinstance(other, ModInt) else
            ModInt(self.x - other)
        )

    def __mul__(self, other):
        return (
            ModInt(self.x * other.x) if isinstance(other, ModInt) else
            ModInt(self.x * other)
        )

    # / : 商。　逆元はフェルマーの小定理を利用している
    def __truediv__(self, other):
        return (
            ModInt(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(self.x * pow(other, MOD - 2, MOD))
        )

    # ** : 指数
    def __pow__(self, other):
        return (
            ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(self.x, other, MOD))
        )

    # x が Modint、y が通常の int の場合に、y.__add__(x) に対して、何を適用するか、定義している（→ x.__add__(y)を呼べ） 
    __radd__ = __add__

    def __rsub__(self, other):
        return (
            ModInt(other.x - self.x) if isinstance(other, ModInt) else
            ModInt(other - self.x)
        )

    __rmul__ = __mul__

    def __rtruediv__(self, other):
        return (
            ModInt(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(other * pow(self.x, MOD - 2, MOD))
        )

    def __rpow__(self, other):
        return (
            ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(other, self.x, MOD))
        )

def cmb(n, r):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return ModInt(fac[n] * facinv[r] * facinv[n-r])

fac = [1, 1] # 元テーブル
facinv = [1, 1] #逆元テーブル
inv = [0, 1] #逆元テーブル計算用テーブル

for i in range(2, N):
    fac.append( ( fac[-1] * i ) % MOD )
    inv.append( ( -inv[MOD % i] * (MOD//i) ) % MOD )
    facinv.append( (facinv[-1] * inv[-1]) % MOD )

# 部分木のDP値を求めていく
# u : 求める頂点
# 親（親側に辿らないように） p

def dfs(u, p = -1):

    global DP, CN, E
    
    tmp_ans = 1
    tmp_cn = 0  # （自分を含む）部分木のノード数

    # u から出ている頂点 v
    for v in E[u]:
        if v != p:  # 親への辺以外について
            DP[v], CN[v] = dfs(v, u)
            tmp_cn += CN[v]
            tmp_ans *= DP[v] * cmb(tmp_cn, CN[v])
    DP[u] = tmp_ans
    CN[u] = tmp_cn + 1
            
    return DP[u], CN[u]

# 各頂点の真のDP値を求めていく

def bfs(u, p=-1):
    
    global DP, E
    
    tmp_ans = DP[u]
    tmp_cn = 1
    
    for v in E[u]:  # 各vに対して「真のDP値」を求めていく
        if v == p:
            continue
            
        # DP[u] と DP[v] から DP[v <- u] を求める
        tmp_cn = N - CN[v]  # v から見たときの u の部分木の要素数
        # print(v+1,tmp_cn)
        tmp_ans = DP[u] / DP[v] / cmb(N - 1, CN[v])
                
        # DP[u <- v] を使って、DP[v] を更新する
        DP[v] = DP[v] * tmp_ans * cmb(N-1, tmp_cn)
        bfs(v, u)
    
    return

# 入力処理
N = int(input())  # 頂点数
E = [[] for _ in range(N)]  # 辺の情報

for _ in range(N - 1):
    a, b = map(int, input().split())
    E[a-1].append(b-1)  # 双方向の情報
    E[b-1].append(a-1)
    
DP = [ModInt(1)] * N
CN = [0] * N

dfs(0)
bfs(0)

for i in DP:
    print(i)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Fri May  8 12:10:59 2020

@author: ybt07
"""

import sys
sys.setrecursionlimit(3*10**5)  # 繰り返し制限

# 組み合わせ
N = 2*10**5   # 問題サイズに合わせて変えておく
MOD = 10**9 + 7

# modint
# https://qiita.com/wotsushi/items/c936838df992b706084c

MOD = 10**9 + 7

class ModInt:
    def __init__(self, x):
        self.x = x % MOD

    def __str__(self):
        return str(self.x)

    __repr__ = __str__

    def __add__(self, other):
        return (
            ModInt(self.x + other.x) if isinstance(other, ModInt) else
            ModInt(self.x + other)
        )

    def __sub__(self, other):
        return (
            ModInt(self.x - other.x) if isinstance(other, ModInt) else
            ModInt(self.x - other)
        )

    def __mul__(self, other):
        return (
            ModInt(self.x * other.x) if isinstance(other, ModInt) else
            ModInt(self.x * other)
        )

    # / : 商。　逆元はフェルマーの小定理を利用している
    def __truediv__(self, other):
        return (
            ModInt(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(self.x * pow(other, MOD - 2, MOD))
        )

    # ** : 指数
    def __pow__(self, other):
        return (
            ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(self.x, other, MOD))
        )

    # x が Modint、y が通常の int の場合に、y.__add__(x) に対して、何を適用するか、定義している（→ x.__add__(y)を呼べ） 
    __radd__ = __add__

    def __rsub__(self, other):
        return (
            ModInt(other.x - self.x) if isinstance(other, ModInt) else
            ModInt(other - self.x)
        )

    __rmul__ = __mul__

    def __rtruediv__(self, other):
        return (
            ModInt(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(other * pow(self.x, MOD - 2, MOD))
        )

    def __rpow__(self, other):
        return (
            ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(other, self.x, MOD))
        )

def cmb(n, r):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return ModInt(fac[n] * facinv[r] * facinv[n-r])

fac = [1, 1] # 元テーブル
facinv = [1, 1] #逆元テーブル
inv = [0, 1] #逆元テーブル計算用テーブル

for i in range(2, N):
    fac.append( ( fac[-1] * i ) % MOD )
    inv.append( ( -inv[MOD % i] * (MOD//i) ) % MOD )
    facinv.append( (facinv[-1] * inv[-1]) % MOD )

# 部分木のDP値を求めていく
# u : 求める頂点
# 親（親側に辿らないように） p

def dfs(u, p = -1):

    global DP, CN, E
    
    tmp_ans = 1
    tmp_cn = 0  # （自分を含む）部分木のノード数

    # u から出ている頂点 v
    for v in E[u]:
        if v != p:  # 親への辺以外について
            DP[v], CN[v] = dfs(v, u)
            tmp_cn += CN[v]
            tmp_ans *= DP[v] * cmb(tmp_cn, CN[v])
    DP[u] = tmp_ans
    CN[u] = tmp_cn + 1
            
    return DP[u], CN[u]

# 各頂点の真のDP値を求めていく

def bfs(u, p=-1):
    
    global DP, E
    
    tmp_ans = DP[u]
    tmp_cn = 1
    
    for v in E[u]:  # 各vに対して「真のDP値」を求めていく
        if v == p:
            continue
            
        # DP[u] と DP[v] から DP[v <- u] を求める
        tmp_cn = N - CN[v]  # v から見たときの u の部分木の要素数
        # print(v+1,tmp_cn)
        tmp_ans = DP[u] / DP[v] / cmb(N - 1, CN[v])
                
        # DP[u <- v] を使って、DP[v] を更新する
        DP[v] = DP[v] * tmp_ans * cmb(N-1, tmp_cn)
        bfs(v, u)
    
    return

# 入力処理
N = int(input())  # 頂点数
E = [[] for _ in range(N)]  # 辺の情報

for _ in range(N - 1):
    a, b = map(int, input().split())
    E[a-1].append(b-1)  # 双方向の情報
    E[b-1].append(a-1)
    
DP = [ModInt(1)] * N
CN = [0] * N

dfs(0)
bfs(0)

for i in DP:
    print(i)

Submission status: Time Limit Exceeded

Solution code:
# From ABC160F
# 各頂点を根としたときのTree DP
# Time Complexity(N)

import sys
sys.setrecursionlimit(200005)

MOD = 10**9+7
class mint:
    def __init__(self, x):
        self.x = x % MOD if isinstance(x, int) else int(x) % MOD
    def __str__(self):
        return str(self.x)
    __repr__ = __str__
    def __iadd__(self, other):
        self.x += other.x if isinstance(other, mint) else other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __isub__(self, other):
        self.x += MOD-other.x if isinstance(other, mint) else MOD-other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __imul__(self, other):
        self.x *= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __imod__(self, other):
        self.x %= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __add__(self, other):
        return (
            mint(self.x + other.x) if isinstance(other, mint) else
            mint(self.x + other)
        )
    def __sub__(self, other):
        return (
            mint(self.x - other.x) if isinstance(other, mint) else
            mint(self.x - other)
        )
    def __mul__(self, other):
        return (
            mint(self.x * other.x) if isinstance(other, mint) else
            mint(self.x * other)
        )
    def __mod__(self, other):
        return (
            mint(self.x % other.x) if isinstance(other, mint) else
            mint(self.x % other)
        )
    def __truediv__(self, other):
        return (
            mint(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(self.x * pow(other, MOD - 2, MOD))
        )
    def __pow__(self, other):
        return (
            mint(pow(self.x, other.x, MOD)) if isinstance(other, mint) else
            mint(pow(self.x, other, MOD))
        )
    __radd__ = __add__
    def __rsub__(self, other):
        return (
            mint(other.x - self.x) if isinstance(other, mint) else
            mint(other - self.x)
        )
    __rmul__ = __mul__
    def __rmod__(self, other):
        return (
            mint(other.x % self.x) if isinstance(other, mint) else
            mint(other % self.x)
        )
    def __rtruediv__(self, other):
        return (
            mint(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(other * pow(self.x, MOD - 2, MOD))
        )
    def __rpow__(self, other):
        return (
            mint(pow(other.x, self.x, MOD)) if isinstance(other, mint) else
            mint(pow(other, self.x, MOD))
        )

class comb():
    # class <mint> should be imported
    def __init__(self, n):
        self.n = n
        fact = [0]*(n+1) # 1-indexed
        ifact = [0]*(n+1) # 逆元
        fact[0] = mint(1)
        for i in range(1, n+1):
            fact[i] = fact[i-1]*i
        ifact[-1] = pow(fact[-1], MOD-2)
        for i in range(n, 0, -1):
            ifact[i-1] = ifact[i]*i
        self.fact = fact
        self.ifact = ifact
    def calc(self, n, k):
        if k<0 or k>n:
            return 0
        return self.fact[n]*self.ifact[k]*self.ifact[n-k]
cb=comb(200005)

# <Edit-here>
class datum:
    def __init__(self, dp=None, size=0):
        self.size = size
        if dp is None:
            self.dp = mint(1)
        else:    
            self.dp = dp

    def merge(self, d):
        res = datum()
        
        res.size = self.size + d.size
        res.dp = self.dp * d.dp
        res.dp *= cb.calc(res.size, self.size)

        return res

    def add_root(self):
        self.size += 1
        return self
        
        # Edit code

# </Edit-here>

def dfs(u,p=-1):
    sumdp = datum()
    for v in to[u]:
        if v == p:
            continue
        dp[u][v] = dfs(v,u)
        sumdp = dp[u][v].merge(sumdp)

    return sumdp.add_root()

def bfs(u,p=-1,dp_p=None):
    if p != -1:
        dp[u][p] = dp_p
    deg = len(to[u])
    SumLeft = [datum() for _ in range(deg+1)]
    SumRight = [datum() for _ in range(deg+1)]
    for i in range(deg):
        SumLeft[i+1] = SumLeft[i].merge(dp[u][to[u][i]])
    for i in reversed(range(1,deg+1)):
        SumRight[i-1] = SumRight[i].merge(dp[u][to[u][i-1]])

    ans[u] = SumLeft[-1].add_root()

    for i in range(deg):
        v = to[u][i]
        if v == p:
            continue
        nxt = SumLeft[i].merge(SumRight[i+1])
        bfs(v,u,nxt.add_root())

# <Input> (Edit if necesarry)
n = int(input())
to = [list() for _ in range(n)]
for i in range(n-1):
    a,b = map(int, input().split())
    a -=  1
    b -= 1
    to[a].append(b)
    to[b].append(a)
# </Input>

ans = [datum() for _ in range(n)]
# dp[u][v]: u->v 方向の部分木
dp = [dict() for _ in range(n)]

dfs(0)
bfs(0)

for i in range(n):
    print(ans[i].dp)

Submission status: Time Limit Exceeded

Solution code:
from copy import deepcopy as copy
import sys
sys.setrecursionlimit(200006)
n = int(input())
MOD = 10**9+7
class mint:
    def __init__(self, x):
        self.x = x % MOD if isinstance(x, int) else int(x) % MOD
    def __str__(self):
        return str(self.x)
    __repr__ = __str__
    def __iadd__(self, other):
        self.x += other.x if isinstance(other, mint) else other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __isub__(self, other):
        self.x += MOD-other.x if isinstance(other, mint) else MOD-other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __imul__(self, other):
        self.x *= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __imod__(self, other):
        self.x %= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __add__(self, other):
        return (
            mint(self.x + other.x) if isinstance(other, mint) else
            mint(self.x + other)
        )
    def __sub__(self, other):
        return (
            mint(self.x - other.x) if isinstance(other, mint) else
            mint(self.x - other)
        )
    def __mul__(self, other):
        return (
            mint(self.x * other.x) if isinstance(other, mint) else
            mint(self.x * other)
        )
    def __mod__(self, other):
        return (
            mint(self.x % other.x) if isinstance(other, mint) else
            mint(self.x % other)
        )
    def __truediv__(self, other):
        return (
            mint(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(self.x * pow(other, MOD - 2, MOD))
        )
    def __pow__(self, other):
        return (
            mint(pow(self.x, other.x, MOD)) if isinstance(other, mint) else
            mint(pow(self.x, other, MOD))
        )
    __radd__ = __add__
    def __rsub__(self, other):
        return (
            mint(other.x - self.x) if isinstance(other, mint) else
            mint(other - self.x)
        )
    __rmul__ = __mul__
    def __rmod__(self, other):
        return (
            mint(other.x % self.x) if isinstance(other, mint) else
            mint(other % self.x)
        )
    def __rtruediv__(self, other):
        return (
            mint(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(other * pow(self.x, MOD - 2, MOD))
        )
    def __rpow__(self, other):
        return (
            mint(pow(other.x, self.x, MOD)) if isinstance(other, mint) else
            mint(pow(other, self.x, MOD))
        )

class comb():
    # class <mint> should be imported
    def __init__(self, n):
        self.n = n
        fact = [0]*(n+1) # 1-indexed
        ifact = [0]*(n+1) # 逆元
        fact[0] = mint(1)
        for i in range(1, n+1):
            fact[i] = fact[i-1]*i
        ifact[-1] = pow(fact[-1], MOD-2)
        for i in range(n, 0, -1):
            ifact[i-1] = ifact[i]*i
        self.fact = fact
        self.ifact = ifact
    def calc(self, n, k):
        if n == 0:
            return 1
        if k<0 or k>n:
            return 0
        return self.fact[n]*self.ifact[k]*self.ifact[n-k]
cb = comb(200005)

class datum:
    def __init__(self, size=0, case=None):
        self.size = size
        if case is None:
            self.case = mint(1)
        else:    
            self.case = case

def merge(d, plus):
    now = copy(d)
    now.size += plus.size
    now.case *= plus.case
    now.case *= cb.ifact[plus.size]
    return now

def add_root(d):
    now = copy(d)
    now.case *= cb.fact[now.size]
    now.size += 1
    return now

def dfs(u,p=-1):
    now = datum()
    for v in to[u]:
        if v == p:
            continue
        dp[u][v] = dfs(v,u)
        now = merge(now,dp[u][v])
    now = add_root(now)
    return now

ans = [mint(0) for _ in range(n)]
def bfs(u,p=-1,pdp=None):
    for v in to[u]:
        if v == p:
            dp[u][v] = pdp
    deg = len(to[u])
    l = [datum() for _ in range(deg+1)]
    r = [datum() for _ in range(deg+1)]
    for i in range(deg):
        l[i+1] = merge(l[i], dp[u][to[u][i]])
    for i in reversed(range(1,deg+1)):
        r[i-1] = merge(r[i], dp[u][to[u][i-1]])

    ans[u] = add_root(l[-1]).case

    for i in range(deg):
        v = to[u][i]
        if v == p:
            continue
        argdp = datum()
        argdp.size += l[i].size + r[i+1].size
        argdp.case *= l[i].case * r[i+1].case
        bfs(v,u,add_root(argdp))







to = [list() for _ in range(n)]
dp = [dict() for _ in range(n)]
for i in range(n-1):
    a,b = map(int, input().split())
    a -=  1
    b -= 1
    to[a].append(b)
    to[b].append(a)

dfs(0)
bfs(0)

print(*ans)

Submission status: Time Limit Exceeded

Solution code:
import sys
sys.setrecursionlimit(200005)
n = int(input())
MOD = 10**9+7
class mint:
    def __init__(self, x):
        self.x = x % MOD if isinstance(x, int) else int(x) % MOD
    def __str__(self):
        return str(self.x)
    __repr__ = __str__
    def __iadd__(self, other):
        self.x += other.x if isinstance(other, mint) else other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __isub__(self, other):
        self.x += MOD-other.x if isinstance(other, mint) else MOD-other
        self.x -= MOD if self.x >= MOD else 0
        return self
    def __imul__(self, other):
        self.x *= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __imod__(self, other):
        self.x %= other.x if isinstance(other, mint) else other
        self.x %= MOD
        return self
    def __add__(self, other):
        return (
            mint(self.x + other.x) if isinstance(other, mint) else
            mint(self.x + other)
        )
    def __sub__(self, other):
        return (
            mint(self.x - other.x) if isinstance(other, mint) else
            mint(self.x - other)
        )
    def __mul__(self, other):
        return (
            mint(self.x * other.x) if isinstance(other, mint) else
            mint(self.x * other)
        )
    def __mod__(self, other):
        return (
            mint(self.x % other.x) if isinstance(other, mint) else
            mint(self.x % other)
        )
    def __truediv__(self, other):
        return (
            mint(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(self.x * pow(other, MOD - 2, MOD))
        )
    def __pow__(self, other):
        return (
            mint(pow(self.x, other.x, MOD)) if isinstance(other, mint) else
            mint(pow(self.x, other, MOD))
        )
    __radd__ = __add__
    def __rsub__(self, other):
        return (
            mint(other.x - self.x) if isinstance(other, mint) else
            mint(other - self.x)
        )
    __rmul__ = __mul__
    def __rmod__(self, other):
        return (
            mint(other.x % self.x) if isinstance(other, mint) else
            mint(other % self.x)
        )
    def __rtruediv__(self, other):
        return (
            mint(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, mint) else
            mint(other * pow(self.x, MOD - 2, MOD))
        )
    def __rpow__(self, other):
        return (
            mint(pow(other.x, self.x, MOD)) if isinstance(other, mint) else
            mint(pow(other, self.x, MOD))
        )

class comb():
    # class <mint> should be imported
    def __init__(self, n):
        self.n = n
        fact = [0]*(n+1) # 1-indexed
        ifact = [0]*(n+1) # 逆元
        fact[0] = mint(1)
        for i in range(1, n+1):
            fact[i] = fact[i-1]*i
        ifact[-1] = pow(fact[-1], MOD-2)
        for i in range(n, 0, -1):
            ifact[i-1] = ifact[i]*i
        self.fact = fact
        self.ifact = ifact
    def calc(self, n, k):
        if n == 0:
            return 1
        if k<0 or k>n:
            return 0
        return self.fact[n]*self.ifact[k]*self.ifact[n-k]
cb = comb(200005)

class datum:
    def __init__(self, size=0, case=None):
        self.size = size
        if case is None:
            self.case = mint(1)
        else:    
            self.case = case

def merge(now, plus):
    ressize = now.size + plus.size
    rescase = now.case*plus.case
    rescase *= cb.ifact[plus.size]
    return datum(ressize,rescase)

def add_root(now):
    rescase = now.case * cb.fact[now.size]
    ressize = now.size + 1
    return datum(ressize,rescase)

def dfs(u,p=-1):
    now = datum()
    for v in to[u]:
        if v == p:
            continue
        dp[u][v] = dfs(v,u)
        now = merge(now,dp[u][v])
    now = add_root(now)
    return now

ans = [mint(0) for _ in range(n)]
def bfs(u,p=-1,pdp=None):
    for v in to[u]:
        if v == p:
            dp[u][v] = pdp
    deg = len(to[u])
    l = [datum() for _ in range(deg+1)]
    r = [datum() for _ in range(deg+1)]
    for i in range(deg):
        l[i+1] = merge(l[i], dp[u][to[u][i]])
    for i in reversed(range(1,deg+1)):
        r[i-1] = merge(r[i], dp[u][to[u][i-1]])

    ans[u] = add_root(l[-1]).case

    for i in range(deg):
        v = to[u][i]
        if v == p:
            continue
        argdp = datum()
        argdp.size += l[i].size + r[i+1].size
        argdp.case *= l[i].case * r[i+1].case
        bfs(v,u,add_root(argdp))







to = [list() for _ in range(n)]
dp = [dict() for _ in range(n)]
for i in range(n-1):
    a,b = map(int, input().split())
    a -=  1
    b -= 1
    to[a].append(b)
    to[b].append(a)

dfs(0)
bfs(0)

print(*ans)