Buggy python submission (verdict: Time Limit Exceeded):
class ReRooting(object):
    """ 全方位木DP """
    def processing(self, in_:list, v:int):
        """ 単項演算(加工) f """
        cnt = in_[0] * factinv[in_[1]] % MOD
        size = in_[1]
        return [cnt, size]
    
    def merge(self, in1:list, in2:list):
        """ 二項演算(マージ) ・ """
        cnt = in1[0] * in2[0] % MOD
        size = in1[1] + in2[1]
        return [cnt, size]

    def adjustment(self, in_:list, v:int):
        """ 単項演算(調整) g """
        cnt = in_[0] * fact[in_[1]] % MOD
        size = in_[1] + 1
        return [cnt, size]
    
    def solve(self):
        """
        計算結果を返す
        
        Ex. [cnt for cnt, _ in self.calc()]
        """
        return [cnt for cnt,_ in self.calc()]

    def __init__(self, V:int, e:list):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
    
    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        accBU = [self.e for _ in range(self.V)]
        resBU = [None] * self.V
        for v in reversed(self.order):
            for c in self.edge[v]:
                accBU[v] = self.merge(accBU[v], self.processing(resBU[c], c))
            resBU[v] = self.adjustment(accBU[v], v)
        return accBU, resBU
    
    def top_down(self, resBU:list):
        """ Top-Down DP """
        accTD = [self.e for _ in range(self.V)]
        resTD = [self.e for _ in range(self.V)]

        for p in self.order:
            ac = self.e if (p == self.order[0]) else self.processing(resTD[p], p)
            for v in self.edge[p]:
                accTD[v] = ac[:]
                ac = self.merge(ac, self.processing(resBU[v], v))
            
            ac = self.e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                resTD[v] = self.adjustment(accTD[v], v)
                ac = self.merge(ac, self.processing(resBU[v], v))
        return resTD
    
    def calc(self):
        self.topological_sort()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)

        res = [None] * self.V
        for v in self.order:
            res[v] = self.e if (v == self.order[0]) else self.processing(resTD[v], v)
            res[v] = self.merge(accBU[v], res[v])
            res[v] = self.adjustment(res[v], v)
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7
 
fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
 
def main():
    RR = ReRooting(N, [1, 0])
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)
    print(*RR.solve(), sep="\n")
 
 
if __name__ == "__main__":
    main()

Fixed submission:
class ReRooting(object):
    """ 全方位木DP """
    def merge(self, a, b):
        """ 二項演算 a・b """
        return a * b % MOD

    def adj_bu(self, accBU, v:int):
        """
        Bottom-Upの単項演算 g(accBU[v])

        v: 頂点
        """
        return accBU * inv(self.SIZE[v]) % MOD

    def adj_td(self, accTD, v:int, p:int):
        """
        Top-Downの単項演算 g(accTD[v])

        v: 頂点
        p: 親
        """
        return accTD * inv(self.V - self.SIZE[v]) % MOD

    def adj_fin(self, acc, v:int):
        """
        最終結果の単項演算 g(acc[v])

        v: 頂点
        """
        return acc * fact[self.V - 1] % MOD

    def __init__(self, V:int, e:int):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
        self.SIZE = [1] * self.V
    
    def subtree_size(self):
        """ 部分木のサイズを求める """
        for v in reversed(self.order[1:]):
            self.SIZE[self.par[v]] += self.SIZE[v]

    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        root = self.order[0]
        accBU = [self.e] * self.V
        resBU = [self.e] * self.V

        for v in reversed(self.order):
            resBU[v] = self.adj_bu(accBU[v], v)

            if v == root: break

            p = self.par[v]
            accBU[p] = self.merge(accBU[p], resBU[v])
        return accBU, resBU
    
    def top_down(self, resBU:list):
        """ Top-Down DP """
        accTD = [self.e] * self.V
        resTD = [self.e] * self.V

        for p in self.order:
            # 左からaccTDを更新
            ac = resTD[p]
            for v in self.edge[p]:
                accTD[v] = ac
                ac = self.merge(ac, resBU[v])

            # 右からaccTDを更新
            ac = self.e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                ac = self.merge(ac, resBU[v])
                
                resTD[v] = self.adj_td(accTD[v], v, p)
        return resTD
    
    def solve(self):
        self.topological_sort()
        self.subtree_size()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)
        res = [self.adj_fin(self.merge(a, b), v) for v,(a,b) in enumerate(zip(accBU, resTD))]
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
inv = lambda n: fact[n - 1] * factinv[n] % MOD # inv[n]: nの逆元

def main():
    RR = ReRooting(N, 1)
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)

    print(*RR.solve(), sep="\n")

if __name__ == "__main__":
    main()

Buggy python submission (verdict: Runtime Error):
class ReRooting(object):
    """ 全方位木DP (オリジナル)"""
    def processing(self, in_:list, v:int):
        """ 単項演算(加工) """
        cnt = in_[0] * factinv[in_[1]] % MOD
        size = in_[1]
        return [cnt, size]
    
    def merge(self, in1:list, in2:list):
        """ 二項演算(マージ) """
        cnt = in1[0] * in2[0] % MOD
        size = in1[1] + in2[1]
        return [cnt, size]

    def adjustment(self, in_:list, v:int):
        """ 単項演算(調整) """
        cnt = in_[0] * fact[in_[1]] % MOD
        size = in_[1] + 1
        return [cnt, size]
    
    def solve(self):
        """ 結果を返す """
        return [cnt for cnt,_ in self.calc()]

    def __init__(self, V:int, e:list):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
    
    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self, e:list):
        """ Bottom-Up DP """
        accBU = [e for _ in range(self.V)]
        resBU = [None] * self.V
        for v in reversed(self.order):
            for c in self.edge[v]:
                accBU[v] = self.merge(accBU[v], self.processing(resBU[c], c))
            resBU[v] = self.adjustment(accBU[v], v)
        return accBU, resBU
    
    def top_down(self, resBU:list, e:list):
        """ Top-Down DP """
        accTD = [e for _ in range(self.V)]
        resTD = [e for _ in range(self.V)]

        for p in self.order:
            ac = self.processing(resTD[p], p)
            for v in self.edge[p]:
                accTD[v] = ac.copy()
                ac = self.merge(ac, self.processing(resBU[v], v))
            
            ac = e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                resTD[v] = self.adjustment(accTD[v], v)
                ac = self.merge(ac, self.processing(resBU[v], v))
        return resTD
    
    def calc(self):
        """ 開始条件: 木を構築済み """
        self.topological_sort()
        accBU, resBU = self.bottom_up(self.e)
        resTD = self.top_down(resBU, self.e)

        res = [None] * self.V
        for v in range(self.V):
            res[v] = self.processing(resTD[v], v)
            res[v] = self.merge(accBU[v], res[v])
            res[v] = self.adjustment(res[v], v)
        return res

#########################################################################################
import sys
input = sys.stdin.readline

N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
 
def main():
    RR = ReRooting(N, [1, 0])
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)
    print(*RR.solve(), sep="\n")

 
if __name__ == "__main__":
    main()

Fixed submission:
class ReRooting(object):
    """ 全方位木DP """
    def merge(self, a, b):
        """ 二項演算 a・b """
        return a * b % MOD

    def adj_bu(self, accBU, v:int):
        """
        Bottom-Upの単項演算 g(accBU[v])

        v: 頂点
        """
        return accBU * inv(self.SIZE[v]) % MOD

    def adj_td(self, accTD, v:int, p:int):
        """
        Top-Downの単項演算 g(accTD[v])

        v: 頂点
        p: 親
        """
        return accTD * inv(self.V - self.SIZE[v]) % MOD

    def adj_fin(self, acc, v:int):
        """
        最終結果の単項演算 g(acc[v])

        v: 頂点
        """
        return acc * fact[self.V - 1] % MOD

    def __init__(self, V:int, e:int):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
        self.SIZE = [1] * self.V
    
    def subtree_size(self):
        """ 部分木のサイズを求める """
        for v in reversed(self.order[1:]):
            self.SIZE[self.par[v]] += self.SIZE[v]

    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        root = self.order[0]
        accBU = [self.e] * self.V
        resBU = [self.e] * self.V

        for v in reversed(self.order):
            resBU[v] = self.adj_bu(accBU[v], v)

            if v == root: break

            p = self.par[v]
            accBU[p] = self.merge(accBU[p], resBU[v])
        return accBU, resBU
    
    def top_down(self, resBU:list):
        """ Top-Down DP """
        accTD = [self.e] * self.V
        resTD = [self.e] * self.V

        for p in self.order:
            # 左からaccTDを更新
            ac = resTD[p]
            for v in self.edge[p]:
                accTD[v] = ac
                ac = self.merge(ac, resBU[v])

            # 右からaccTDを更新
            ac = self.e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                ac = self.merge(ac, resBU[v])
                
                resTD[v] = self.adj_td(accTD[v], v, p)
        return resTD
    
    def solve(self):
        self.topological_sort()
        self.subtree_size()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)
        res = [self.adj_fin(self.merge(a, b), v) for v,(a,b) in enumerate(zip(accBU, resTD))]
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
inv = lambda n: fact[n - 1] * factinv[n] % MOD # inv[n]: nの逆元

def main():
    RR = ReRooting(N, 1)
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)

    print(*RR.solve(), sep="\n")

if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class ReRooting(object):
    """ 全方位木DP (オリジナル)"""
    def processing(self, in_:list, v:int):
        """ 単項演算(加工) """
        cnt = in_[0] * factinv[in_[1]] % MOD
        size = in_[1]
        return [cnt, size]
    
    def merge(self, in1:list, in2:list):
        """ 二項演算(マージ) """
        cnt = in1[0] * in2[0] % MOD
        size = in1[1] + in2[1]
        return [cnt, size]

    def adjustment(self, in_:list, v:int):
        """ 単項演算(調整) """
        cnt = in_[0] * fact[in_[1]] % MOD
        size = in_[1] + 1
        return [cnt, size]
    
    def solve(self):
        """ 結果を返す """
        return [cnt for cnt,_ in self.calc()]

    def __init__(self, V:int, e:list):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
    
    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self, e:list):
        """ Bottom-Up DP """
        accBU = [e for _ in range(self.V)]
        resBU = [None] * self.V
        for v in reversed(self.order):
            for c in self.edge[v]:
                accBU[v] = self.merge(accBU[v], self.processing(resBU[c], c))
            resBU[v] = self.adjustment(accBU[v], v)
        return accBU, resBU
    
    def top_down(self, resBU:list, e:list):
        """ Top-Down DP """
        accTD = [e for _ in range(self.V)]
        resTD = [e for _ in range(self.V)]

        for p in self.order:
            ac = self.processing(resTD[p], p)
            for v in self.edge[p]:
                accTD[v] = ac.copy()
                ac = self.merge(ac, self.processing(resBU[v], v))
            
            ac = e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                resTD[v] = self.adjustment(accTD[v], v)
                ac = self.merge(ac, self.processing(resBU[v], v))
        return resTD
    
    def calc(self):
        """ 開始条件: 木を構築済み """
        self.topological_sort()
        accBU, resBU = self.bottom_up(self.e)
        resTD = self.top_down(resBU, self.e)

        res = [None] * self.V
        for v in range(self.V):
            res[v] = self.processing(resTD[v], v)
            res[v] = self.merge(accBU[v], res[v])
            res[v] = self.adjustment(res[v], v)
        return res

#########################################################################################
import sys
input = sys.stdin.readline

N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
 
def main():
    RR = ReRooting(N, [1, 0])
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)
    print(*RR.solve(), sep="\n")

 
if __name__ == "__main__":
    main()

Fixed submission:
class ReRooting(object):
    """ 全方位木DP """
    def merge(self, a, b):
        """ 二項演算 a・b """
        return a * b % MOD

    def adj_bu(self, accBU, v:int):
        """
        Bottom-Upの単項演算 g(accBU[v])

        v: 頂点
        """
        return accBU * inv(self.SIZE[v]) % MOD

    def adj_td(self, accTD, v:int, p:int):
        """
        Top-Downの単項演算 g(accTD[v])

        v: 頂点
        p: 親
        """
        return accTD * inv(self.V - self.SIZE[v]) % MOD

    def adj_fin(self, acc, v:int):
        """
        最終結果の単項演算 g(acc[v])

        v: 頂点
        """
        return acc * fact[self.V - 1] % MOD

    def __init__(self, V:int, e:int):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
        self.SIZE = [1] * self.V
    
    def subtree_size(self):
        """ 部分木のサイズを求める """
        for v in reversed(self.order[1:]):
            self.SIZE[self.par[v]] += self.SIZE[v]

    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        root = self.order[0]
        accBU = [self.e] * self.V
        resBU = [self.e] * self.V

        for v in reversed(self.order):
            resBU[v] = self.adj_bu(accBU[v], v)

            if v == root: break

            p = self.par[v]
            accBU[p] = self.merge(accBU[p], resBU[v])
        return accBU, resBU
    
    def top_down(self, resBU:list):
        """ Top-Down DP """
        accTD = [self.e] * self.V
        resTD = [self.e] * self.V

        for p in self.order:
            # 左からaccTDを更新
            ac = resTD[p]
            for v in self.edge[p]:
                accTD[v] = ac
                ac = self.merge(ac, resBU[v])

            # 右からaccTDを更新
            ac = self.e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                ac = self.merge(ac, resBU[v])
                
                resTD[v] = self.adj_td(accTD[v], v, p)
        return resTD
    
    def solve(self):
        self.topological_sort()
        self.subtree_size()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)
        res = [self.adj_fin(self.merge(a, b), v) for v,(a,b) in enumerate(zip(accBU, resTD))]
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
inv = lambda n: fact[n - 1] * factinv[n] % MOD # inv[n]: nの逆元

def main():
    RR = ReRooting(N, 1)
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)

    print(*RR.solve(), sep="\n")

if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class ReRooting(object):
    """ 全方位木DP (オリジナル)"""
    def processing(self, in_:dict, v:int):
        """ 単項演算(加工) """
        cnt = in_["cnt"] * factinv[in_["size"]] % MOD
        size = in_["size"]
        return {"cnt":cnt, "size":size}
    
    def merge(self, in1:dict, in2:dict):
        """ 二項演算(マージ) """
        cnt = in1["cnt"] * in2["cnt"] % MOD
        size = in1["size"] + in2["size"]
        return {"cnt":cnt, "size":size}

    def adjustment(self, in_:dict, v:int):
        """ 単項演算(調整) """
        cnt = in_["cnt"] * fact[in_["size"]] % MOD
        size = in_["size"] + 1
        return {"cnt":cnt, "size":size}
    
    def solve(self):
        """ 結果を返す """
        ans = self.calc()
        for v in range(self.V):
            ans[v] = ans[v]["cnt"]
        return ans

    def __init__(self, V:int, e:dict):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
    
    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self, e:dict):
        """ Bottom-Up DP """
        accBU = [e for _ in range(self.V)]
        resBU = [None] * self.V
        for v in reversed(self.order):
            for c in self.edge[v]:
                accBU[v] = self.merge(accBU[v], self.processing(resBU[c], c))
            resBU[v] = self.adjustment(accBU[v], v)
        return accBU, resBU
    
    def top_down(self, resBU:dict, e:dict):
        """ Top-Down DP """
        accTD = [e for _ in range(self.V)]
        resTD = [e for _ in range(self.V)]

        for p in self.order:
            ac = self.processing(resTD[p], p)
            for v in self.edge[p]:
                accTD[v] = ac.copy()
                ac = self.merge(ac, self.processing(resBU[v], v))
            
            ac = self.e.copy()
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                resTD[v] = self.adjustment(accTD[v], v)
                ac = self.merge(ac, self.processing(resBU[v], v))
        return resTD
    
    def calc(self):
        """ 開始条件: 木を構築済み """
        self.topological_sort()
        accBU, resBU = self.bottom_up(self.e)
        resTD = self.top_down(resBU, self.e)

        res = [None] * self.V
        for v in range(self.V):
            res[v] = self.processing(resTD[v], v)
            res[v] = self.merge(accBU[v], res[v])
            res[v] = self.adjustment(res[v], v)
        return res

#########################################################################################
import sys
input = sys.stdin.readline

N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
 
def main():
    RR = ReRooting(N, {"cnt":1, "size":0})
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)
    print(*RR.solve(), sep="\n")

 
if __name__ == "__main__":
    main()

Fixed submission:
class ReRooting(object):
    """ 全方位木DP """
    def merge(self, a, b):
        """ 二項演算 a・b """
        return a * b % MOD

    def adj_bu(self, accBU, v:int):
        """
        Bottom-Upの単項演算 g(accBU[v])

        v: 頂点
        """
        return accBU * inv(self.SIZE[v]) % MOD

    def adj_td(self, accTD, v:int, p:int):
        """
        Top-Downの単項演算 g(accTD[v])

        v: 頂点
        p: 親
        """
        return accTD * inv(self.V - self.SIZE[v]) % MOD

    def adj_fin(self, acc, v:int):
        """
        最終結果の単項演算 g(acc[v])

        v: 頂点
        """
        return acc * fact[self.V - 1] % MOD

    def __init__(self, V:int, e:int):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
        self.SIZE = [1] * self.V
    
    def subtree_size(self):
        """ 部分木のサイズを求める """
        for v in reversed(self.order[1:]):
            self.SIZE[self.par[v]] += self.SIZE[v]

    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        root = self.order[0]
        accBU = [self.e] * self.V
        resBU = [self.e] * self.V

        for v in reversed(self.order):
            resBU[v] = self.adj_bu(accBU[v], v)

            if v == root: break

            p = self.par[v]
            accBU[p] = self.merge(accBU[p], resBU[v])
        return accBU, resBU
    
    def top_down(self, resBU:list):
        """ Top-Down DP """
        accTD = [self.e] * self.V
        resTD = [self.e] * self.V

        for p in self.order:
            # 左からaccTDを更新
            ac = resTD[p]
            for v in self.edge[p]:
                accTD[v] = ac
                ac = self.merge(ac, resBU[v])

            # 右からaccTDを更新
            ac = self.e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                ac = self.merge(ac, resBU[v])
                
                resTD[v] = self.adj_td(accTD[v], v, p)
        return resTD
    
    def solve(self):
        self.topological_sort()
        self.subtree_size()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)
        res = [self.adj_fin(self.merge(a, b), v) for v,(a,b) in enumerate(zip(accBU, resTD))]
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
inv = lambda n: fact[n - 1] * factinv[n] % MOD # inv[n]: nの逆元

def main():
    RR = ReRooting(N, 1)
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)

    print(*RR.solve(), sep="\n")

if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class ReRooting(object):
    """ 全方位木DP (オリジナル)"""
    def processing(self, in_:dict, v:int):
        """ 単項演算(加工) """
        cnt = in_["cnt"] * factinv[in_["size"]] % MOD
        size = in_["size"]
        return {"cnt":cnt, "size":size}
    
    def merge(self, in1:dict, in2:dict):
        """ 二項演算(マージ) """
        cnt = in1["cnt"] * in2["cnt"] % MOD
        size = in1["size"] + in2["size"]
        return {"cnt":cnt, "size":size}

    def adjustment(self, in_:dict, v:int):
        """ 単項演算(調整) """
        cnt = in_["cnt"] * fact[in_["size"]] % MOD
        size = in_["size"] + 1
        return {"cnt":cnt, "size":size}
    
    def solve(self):
        """ 結果を返す """
        ans = self.calc()
        for v in range(self.V):
            ans[v] = ans[v]["cnt"]
        return ans

    def __init__(self, V:int, e:dict):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
    
    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        accBU = [self.e.copy() for _ in range(self.V)]
        resBU = [None] * self.V
        for v in reversed(self.order):
            for c in self.edge[v]:
                accBU[v] = self.merge(accBU[v], self.processing(resBU[c], c))
            resBU[v] = self.adjustment(accBU[v], v)
        return accBU, resBU
    
    def top_down(self, resBU:dict):
        """ Top-Down DP """
        accTD = [self.e.copy() for _ in range(self.V)]
        resTD = [self.e.copy() for _ in range(self.V)]

        for p in self.order:
            ac = self.processing(resTD[p], p)
            for v in self.edge[p]:
                accTD[v] = ac.copy()
                ac = self.merge(ac, self.processing(resBU[v], v))
            
            ac = self.e.copy()
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                resTD[v] = self.adjustment(accTD[v], v)
                ac = self.merge(ac, self.processing(resBU[v], v))
        return resTD
    
    def calc(self):
        """ 開始条件: 木を構築済み """
        self.topological_sort()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)

        res = [None] * self.V
        for v in range(self.V):
            res[v] = self.processing(resTD[v], v)
            res[v] = self.merge(accBU[v], res[v])
            res[v] = self.adjustment(res[v], v)
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7
 
fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
 
def main():
    RR = ReRooting(N, {"cnt":1, "size":0})
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)
    print(*RR.solve(), sep="\n")

 
if __name__ == "__main__":
    main()

Fixed submission:
class ReRooting(object):
    """ 全方位木DP """
    def merge(self, a, b):
        """ 二項演算 a・b """
        return a * b % MOD

    def adj_bu(self, accBU, v:int):
        """
        Bottom-Upの単項演算 g(accBU[v])

        v: 頂点
        """
        return accBU * inv(self.SIZE[v]) % MOD

    def adj_td(self, accTD, v:int, p:int):
        """
        Top-Downの単項演算 g(accTD[v])

        v: 頂点
        p: 親
        """
        return accTD * inv(self.V - self.SIZE[v]) % MOD

    def adj_fin(self, acc, v:int):
        """
        最終結果の単項演算 g(acc[v])

        v: 頂点
        """
        return acc * fact[self.V - 1] % MOD

    def __init__(self, V:int, e:int):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
        self.SIZE = [1] * self.V
    
    def subtree_size(self):
        """ 部分木のサイズを求める """
        for v in reversed(self.order[1:]):
            self.SIZE[self.par[v]] += self.SIZE[v]

    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        root = self.order[0]
        accBU = [self.e] * self.V
        resBU = [self.e] * self.V

        for v in reversed(self.order):
            resBU[v] = self.adj_bu(accBU[v], v)

            if v == root: break

            p = self.par[v]
            accBU[p] = self.merge(accBU[p], resBU[v])
        return accBU, resBU
    
    def top_down(self, resBU:list):
        """ Top-Down DP """
        accTD = [self.e] * self.V
        resTD = [self.e] * self.V

        for p in self.order:
            # 左からaccTDを更新
            ac = resTD[p]
            for v in self.edge[p]:
                accTD[v] = ac
                ac = self.merge(ac, resBU[v])

            # 右からaccTDを更新
            ac = self.e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                ac = self.merge(ac, resBU[v])
                
                resTD[v] = self.adj_td(accTD[v], v, p)
        return resTD
    
    def solve(self):
        self.topological_sort()
        self.subtree_size()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)
        res = [self.adj_fin(self.merge(a, b), v) for v,(a,b) in enumerate(zip(accBU, resTD))]
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
inv = lambda n: fact[n - 1] * factinv[n] % MOD # inv[n]: nの逆元

def main():
    RR = ReRooting(N, 1)
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)

    print(*RR.solve(), sep="\n")

if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class ReRooting(object):
    """ 全方位木DP (オリジナル)"""
    def processing(self, in_:dict, v:int):
        """ 単項演算(加工) """
        out = self.e.copy()
        out["cnt"] = in_["cnt"] * factinv[in_["size"]] % MOD
        out["size"] = in_["size"]
        return out
    
    def merge(self, in1:dict, in2:dict):
        """ 二項演算(マージ) """
        out = self.e.copy()
        out["cnt"] = in1["cnt"] * in2["cnt"] % MOD
        out["size"] = in1["size"] + in2["size"]
        return out

    def adjustment(self, in_:dict, v:int):
        """ 単項演算(調整) """
        out = self.e.copy()
        out["cnt"] = in_["cnt"] * fact[in_["size"]] % MOD
        out["size"] = in_["size"] + 1
        return out
    
    def solve(self):
        """ 結果を返す """
        ans = self.calc()
        for v in range(self.V):
            ans[v] = ans[v]["cnt"]
        return ans

    def __init__(self, V:int, e:dict):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
    
    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        accBU = [self.e.copy() for _ in range(self.V)]
        resBU = [None] * self.V
        for v in reversed(self.order):
            for c in self.edge[v]:
                accBU[v] = self.merge(accBU[v], self.processing(resBU[c], c))
            resBU[v] = self.adjustment(accBU[v], v)
        return accBU, resBU
    
    def top_down(self, resBU:dict):
        """ Top-Down DP """
        accTD = [self.e.copy() for _ in range(self.V)]
        resTD = [self.e.copy() for _ in range(self.V)]

        for p in self.order:
            ac = self.processing(resTD[p], p)
            for v in self.edge[p]:
                accTD[v] = ac.copy()
                ac = self.merge(ac, self.processing(resBU[v], v))
            
            ac = self.e.copy()
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                resTD[v] = self.adjustment(accTD[v], v)
                ac = self.merge(ac, self.processing(resBU[v], v))
        return resTD
    
    def calc(self):
        """ 開始条件: 木を構築済み """
        self.topological_sort()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)

        res = [None] * self.V
        for v in range(self.V):
            res[v] = self.processing(resTD[v], v)
            res[v] = self.merge(accBU[v], res[v])
            res[v] = self.adjustment(res[v], v)
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7
 
fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
 
def main():
    RR = ReRooting(N, {"cnt":1, "size":0})
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)
    print(*RR.solve(), sep="\n")

 
if __name__ == "__main__":
    main()

Fixed submission:
class ReRooting(object):
    """ 全方位木DP """
    def merge(self, a, b):
        """ 二項演算 a・b """
        return a * b % MOD

    def adj_bu(self, accBU, v:int):
        """
        Bottom-Upの単項演算 g(accBU[v])

        v: 頂点
        """
        return accBU * inv(self.SIZE[v]) % MOD

    def adj_td(self, accTD, v:int, p:int):
        """
        Top-Downの単項演算 g(accTD[v])

        v: 頂点
        p: 親
        """
        return accTD * inv(self.V - self.SIZE[v]) % MOD

    def adj_fin(self, acc, v:int):
        """
        最終結果の単項演算 g(acc[v])

        v: 頂点
        """
        return acc * fact[self.V - 1] % MOD

    def __init__(self, V:int, e:int):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
        self.SIZE = [1] * self.V
    
    def subtree_size(self):
        """ 部分木のサイズを求める """
        for v in reversed(self.order[1:]):
            self.SIZE[self.par[v]] += self.SIZE[v]

    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        root = self.order[0]
        accBU = [self.e] * self.V
        resBU = [self.e] * self.V

        for v in reversed(self.order):
            resBU[v] = self.adj_bu(accBU[v], v)

            if v == root: break

            p = self.par[v]
            accBU[p] = self.merge(accBU[p], resBU[v])
        return accBU, resBU
    
    def top_down(self, resBU:list):
        """ Top-Down DP """
        accTD = [self.e] * self.V
        resTD = [self.e] * self.V

        for p in self.order:
            # 左からaccTDを更新
            ac = resTD[p]
            for v in self.edge[p]:
                accTD[v] = ac
                ac = self.merge(ac, resBU[v])

            # 右からaccTDを更新
            ac = self.e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                ac = self.merge(ac, resBU[v])
                
                resTD[v] = self.adj_td(accTD[v], v, p)
        return resTD
    
    def solve(self):
        self.topological_sort()
        self.subtree_size()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)
        res = [self.adj_fin(self.merge(a, b), v) for v,(a,b) in enumerate(zip(accBU, resTD))]
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
inv = lambda n: fact[n - 1] * factinv[n] % MOD # inv[n]: nの逆元

def main():
    RR = ReRooting(N, 1)
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)

    print(*RR.solve(), sep="\n")

if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
class ReRooting(object):
    """ 全方位木DP (オリジナル)"""
    def processing(self, in_:dict, v:int):
        """ 単項演算(加工) """
        out = self.e.copy()
        out["cnt"] = in_["cnt"] * factinv[in_["size"]] % MOD
        out["size"] = in_["size"]
        return out
    
    def merge(self, in1:dict, in2:dict):
        """ 二項演算(マージ) """
        out = self.e.copy()
        out["cnt"] = in1["cnt"] * in2["cnt"] % MOD
        out["size"] = in1["size"] + in2["size"]
        return out

    def adjustment(self, in_:dict, v:int):
        """ 単項演算(調整) """
        out = self.e.copy()
        out["cnt"] = in_["cnt"] * fact[in_["size"]] % MOD
        out["size"] = in_["size"] + 1
        return out
    
    def solve(self):
        """ 結果を返す """
        ans = self.calc()
        for v in range(self.V):
            ans[v] = ans[v]["cnt"]
        return ans

    def __init__(self, V:int, e:dict):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
    
    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        accBU = [self.e.copy() for _ in range(self.V)]
        resBU = [None] * self.V
        for v in reversed(self.order):
            for c in self.edge[v]:
                accBU[v] = self.merge(accBU[v], self.processing(resBU[c], c))
            resBU[v] = self.adjustment(accBU[v], v)
        return accBU, resBU
    
    def top_down(self, resBU:dict):
        """ Top-Down DP """
        accTD = [self.e.copy() for _ in range(self.V)]
        resTD = [self.e.copy() for _ in range(self.V)]

        for p in self.order:
            ac = self.processing(resTD[p], p)
            for v in self.edge[p]:
                accTD[v] = ac.copy()
                ac = self.merge(ac, self.processing(resBU[v], v))
            
            ac = self.e.copy()
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                resTD[v] = self.adjustment(accTD[v], v)
                ac = self.merge(ac, self.processing(resBU[v], v))
        return resTD
    
    def calc(self):
        """ 開始条件: 木を構築済み """
        self.topological_sort()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)

        res = [None] * self.V
        for v in range(self.V):
            res[v] = self.processing(resTD[v], v)
            res[v] = self.merge(accBU[v], res[v])
            res[v] = self.adjustment(res[v], v)
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7
 
fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
 
def main():
    RR = ReRooting(N, {"cnt":1, "size":0})
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)
    print(*RR.solve(), sep="\n")

 
if __name__ == "__main__":
    main()

Fixed submission:
class ReRooting(object):
    """ 全方位木DP """
    def merge(self, a, b):
        """ 二項演算 a・b """
        return a * b % MOD

    def adj_bu(self, accBU, v:int):
        """
        Bottom-Upの単項演算 g(accBU[v])

        v: 頂点
        """
        return accBU * inv(self.SIZE[v]) % MOD

    def adj_td(self, accTD, v:int, p:int):
        """
        Top-Downの単項演算 g(accTD[v])

        v: 頂点
        p: 親
        """
        return accTD * inv(self.V - self.SIZE[v]) % MOD

    def adj_fin(self, acc, v:int):
        """
        最終結果の単項演算 g(acc[v])

        v: 頂点
        """
        return acc * fact[self.V - 1] % MOD

    def __init__(self, V:int, e:int):
        """
        V: 頂点数
        e: 単位元
        """
        self.V, self.e = V, e
        self.edge = [[] for _ in range(V)]
        self.par = [-1] * V
        self.order = []
        self.SIZE = [1] * self.V
    
    def subtree_size(self):
        """ 部分木のサイズを求める """
        for v in reversed(self.order[1:]):
            self.SIZE[self.par[v]] += self.SIZE[v]

    def add_edge(self, u:int, v:int):
        """ 辺(u,v)をグラフに追加する """
        self.edge[u].append(v)
        self.edge[v].append(u)
    
    def topological_sort(self, root:int = 0):
        """ トポロジカルソート """
        from collections import deque
        que = deque([root])
        while que:
            v = que.popleft()
            self.order.append(v)
            for w in self.edge[v]:
                if w != self.par[v]:
                    self.par[w] = v
                    self.edge[w].remove(v)
                    que.append(w)
    
    def bottom_up(self):
        """ Bottom-Up DP """
        root = self.order[0]
        accBU = [self.e] * self.V
        resBU = [self.e] * self.V

        for v in reversed(self.order):
            resBU[v] = self.adj_bu(accBU[v], v)

            if v == root: break

            p = self.par[v]
            accBU[p] = self.merge(accBU[p], resBU[v])
        return accBU, resBU
    
    def top_down(self, resBU:list):
        """ Top-Down DP """
        accTD = [self.e] * self.V
        resTD = [self.e] * self.V

        for p in self.order:
            # 左からaccTDを更新
            ac = resTD[p]
            for v in self.edge[p]:
                accTD[v] = ac
                ac = self.merge(ac, resBU[v])

            # 右からaccTDを更新
            ac = self.e
            for v in reversed(self.edge[p]):
                accTD[v] = self.merge(accTD[v], ac)
                ac = self.merge(ac, resBU[v])
                
                resTD[v] = self.adj_td(accTD[v], v, p)
        return resTD
    
    def solve(self):
        self.topological_sort()
        self.subtree_size()
        accBU, resBU = self.bottom_up()
        resTD = self.top_down(resBU)
        res = [self.adj_fin(self.merge(a, b), v) for v,(a,b) in enumerate(zip(accBU, resTD))]
        return res

#########################################################################################
N = int(input())
MOD = 10 ** 9 + 7

fact = [1] * (N + 1) # fact[n]: n!
factinv = [1] * (N + 1) # n!の逆元
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % MOD
factinv[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, -1, -1):
    factinv[i] = factinv[i + 1] * (i + 1) % MOD
inv = lambda n: fact[n - 1] * factinv[n] % MOD # inv[n]: nの逆元

def main():
    RR = ReRooting(N, 1)
    for _ in range(N - 1):
        a, b = map(int, input().split())
        RR.add_edge(a - 1, b- 1)

    print(*RR.solve(), sep="\n")

if __name__ == "__main__":
    main()