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: Accepted

Solution code:
#%%
import sys
sys.setrecursionlimit(10**7) #再帰関数の上限,10**5以上の場合python
import math

#heapify(q),heappush(q,a),heappop(q) #q=heapify(q)としないこと、返り値はNone
#import fractions#古いatcoderコンテストの場合GCDなどはここからimportする
from functools import lru_cache#pypyでもうごく
#@lru_cache(maxsize = None)#maxsizeは保存するデータ数の最大値、2**nが最も高効率


def input(): return sys.stdin.readline()[:-1]
def printl(li): _=print(*li, sep="\n") if li else None
def argsort(s, return_sorted=False): 
    inds=sorted(range(len(s)), key=lambda k: s[k])
    if return_sorted: return inds, [s[i] for i in inds]
    return inds
def alp2num(c,cap=False): return ord(c)-97 if not cap else ord(c)-65
def num2alp(i,cap=False): return chr(i+97) if not cap else chr(i+65)
def matmat(A,B):
    K,N,M=len(B),len(A),len(B[0])
    return [[sum([(A[i][k]*B[k][j]) for k in range(K)]) for j in range(M)] for i in range(N)]
def matvec(M,v):
    N,size=len(v),len(M)
    return [sum([M[i][j]*v[j] for j in range(N)]) for i in range(size)]
def T(M):
    n,m=len(M),len(M[0])
    return [[M[j][i] for j in range(n)] for i in range(m)]

    
class modint:#add:和,mul:積,pow:累乗,div:商(modと互いに素であること)
    def __init__(self,x,mod=1000000007): 
        if isinstance(x, modint):x=x.x
        self.x, self.mod= x%mod, mod

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

    def __add__(self, a):
        if isinstance(a, modint):a=a.x
        return modint(self.x+a,self.mod)

    def __radd__(self, a):return self.__add__(a)

    def __iadd__(self, a):
        self.x=self.__add__(a)
        return self

    def __sub__(self, a):
        if isinstance(a, modint):a=a.x
        return self.__add__(-a)
    
    def __rsub__(self, a):return (a-self.x)%mod

    def __isub__(self, a):
        return self.__iadd__(-a)

    def __mul__(self, c):
        if isinstance(c, modint):c=c.x
        return modint(self.x*(c%self.mod),self.mod)
    
    def __rmul__(self, c):return self.__mul__(c)
    
    def __imul__(self, c):
        return self.__mul__(c)

    def __pow__(self,p):
        if isinstance(p, modint):p=p.x
        return modint(pow(self.x,p,self.mod),self.mod)
    
    def __ipow__(self,p):
        return self.__pow__(p)
        

    def __truediv__(self, d):
        if isinstance(d, modint):d=d.x
        u,v,a,b=1,0,d,self.mod
        while b:
            t=a//b
            a-=t*b
            a,b,u,v=b,a,v,u-t*v
        if a!=1: print("not 素")
        return modint(self.x*(u%self.mod),self.mod)

    def __itruediv__(self, d):
        self.x=self.__truediv__(d)
        return self

    def __eq__(self, target):
        if isinstance(target, modint):
            return self.x==target.x
        return self.x==target%self.mod
    
        
class comb:
    def __init__(self,N,mod=10**9+7):#コンビネーションnCrをmodで求める、Nは最大のn 
        self.mod=mod
        self.fact=[0]*(N+1)
        self.ifact=[0]*(N+1)
        fact,ifact=self.fact,self.ifact
        fact[0],fact[1],ifact[0],ifact[1]=1,1,1,1
        for i in range(2,N+1):
            x=(fact[i-1]*i)%mod
            fact[i]=x
            ifact[i]=self.extgcd1(x,mod)
        

    #@lru_cache(maxsize = None)
    def extgcd1(self,a0,b0):#計算量log(b0),フェルマーの小定理より早い
        u,v,a,b=1,0,a0,b0
        while b:
            t,a=divmod(a,b)
            a,b,u,v=b,a,v,u-t*v
        if a!=1: 
            print("not 素")
            return -1
        return u%b0

    #@lru_cache(maxsize = None)
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    #@lru_cache(maxsize = None)
    def mulcomb(self,n,*rs):#n!/(r1!*r2!*r3!*...)
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:#全方位木
    def __init__(self,N,edge):#単位元self.unitとモノイドdef funcを設定すること,
        #dics[親][根（親の隣接点)]=その部分木での値
        self.unit=(modint(1),0)
        self.mod=10**9+7
        self.edge=edge
        self.cb=comb(N)
        self.fact=self.cb.fact
        self.ifact=self.cb.ifact
        self.par=[-1]*N
        self.N=N
        self.visited=[0]*N
        self.dics=[dict() for _ in range(N)]
        self.ikigake=[]
        self.tot=[self.unit]*N
    
    #@lru_cache(maxsize = None)
    def func(self,x,y):
        #ifact=self.ifact
        #mod=self.mod
        p1,s1=x
        p2,s2=y
        ans=modint(p1*p2)
        ssum=s1+s2
        ans*=self.cb.comb(ssum,s1)
        #ans*=(self.fact[ssum]*self.ifact[s1])%self.mod*self.ifact[s2]%self.mod
        #ans%=self.mod
        return ans,ssum 

    def addnode(self,x):#部分木に親のノードを結合する処理,dfsとforwardに出現
        return x[0],x[1]+1

    def _dfs(self,e,pa):
        edge=self.edge
        self.par[e]=pa
        self.ikigake.append(e)
        ans=self.unit
        for ne in edge[e]:
            if self.par[ne]!=-1:
                continue
            ans=self.func(ans,self.addnode(self._dfs(ne,e)))
            #print(ans)
        if pa!=e:
            self.dics[pa][e]=ans
        
        return ans
    
    def forward(self,start):
        self._dfs(start,start)
        #print(t2-t1)
        #count=0
        for e in self.ikigake:
            pa=self.par[e]
            de=self.dics[e]
            nes=tuple(de.keys())
            nvals=tuple(de.values())
            l=len(nes)
            aleft=[self.unit]
            aright=[self.unit]
            cleft=self.unit
            cright=self.unit
            for i in range(l-1):
                aleft.append(self.func(aleft[-1],self.addnode(nvals[i])))
                aright.append(self.func(aright[-1],self.addnode(nvals[-i-1])))
                #count+=4
            self.tot[e]=self.func(aright[-1],self.addnode(nvals[0]))
            for i,ne in enumerate(nes):
                if ne==pa:
                    continue
                self.dics[ne][e]=self.func(aleft[i],aright[-1-i])
                #count+=1
        #print(t3-t2)

def main():
    mod = 1000000007
    #w.sort(key=itemgetter(1),reversed=True)  #二個目の要素で降順並び替え

    N = int(input())
    #N, K = map(int, input().split())
    #A = tuple(map(int, input().split())) #1行ベクトル
    #L = tuple(int(input()) for i in range(N)) #改行ベクトル
    #S = tuple(tuple(map(int, input().split())) for i in range(N)) #改行行列

    def tree_init(N):
        edgelist = [[] for _ in range(N)]
        elist=set()
        for a, b in [map(int, input().split()) for i in range(N-1)]:#木じゃない場合N-1をNに変える
            edgelist[a-1].append(b-1)#ノードの番号が0から始まる場合-1を消す
            edgelist[b-1].append(a-1)
            elist.add((a-1,b-1))
        return edgelist,elist

    edge,elist=tree_init(N)
    cb=comb(N)
    rt=rerooting(N,edge)
    rt.forward(0)

    for a in range(N):
        print(rt.tot[a][0])

if __name__ == "__main__":
    main()

#%%

Submission status: Accepted

Solution code:
#%%
import sys
sys.setrecursionlimit(10**7) #再帰関数の上限,10**5以上の場合python
import math

#heapify(q),heappush(q,a),heappop(q) #q=heapify(q)としないこと、返り値はNone
#import fractions#古いatcoderコンテストの場合GCDなどはここからimportする
from functools import lru_cache#pypyでもうごく
#@lru_cache(maxsize = None)#maxsizeは保存するデータ数の最大値、2**nが最も高効率


def input(): return sys.stdin.readline()[:-1]
def printl(li): _=print(*li, sep="\n") if li else None
def argsort(s, return_sorted=False): 
    inds=sorted(range(len(s)), key=lambda k: s[k])
    if return_sorted: return inds, [s[i] for i in inds]
    return inds
def alp2num(c,cap=False): return ord(c)-97 if not cap else ord(c)-65
def num2alp(i,cap=False): return chr(i+97) if not cap else chr(i+65)
def matmat(A,B):
    K,N,M=len(B),len(A),len(B[0])
    return [[sum([(A[i][k]*B[k][j]) for k in range(K)]) for j in range(M)] for i in range(N)]
def matvec(M,v):
    N,size=len(v),len(M)
    return [sum([M[i][j]*v[j] for j in range(N)]) for i in range(size)]
def T(M):
    n,m=len(M),len(M[0])
    return [[M[j][i] for j in range(n)] for i in range(m)]

        
class comb:
    def __init__(self,N,mod=10**9+7):#コンビネーションnCrをmodで求める、Nは最大のn 
        self.mod=mod
        self.fact=[0]*(N+1)
        self.ifact=[0]*(N+1)
        fact,ifact=self.fact,self.ifact
        fact[0],fact[1],ifact[0],ifact[1]=1,1,1,1
        for i in range(2,N+1):
            x=(fact[i-1]*i)%mod
            fact[i]=x
            ifact[i]=self.extgcd1(x,mod)
        

    #@lru_cache(maxsize = None)
    def extgcd1(self,a0,b0):#計算量log(b0),フェルマーの小定理より早い
        u,v,a,b=1,0,a0,b0
        while b:
            t,a=divmod(a,b)
            a,b,u,v=b,a,v,u-t*v
        if a!=1: 
            print("not 素")
            return -1
        return u%b0

    #@lru_cache(maxsize = None)
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    @lru_cache(maxsize = None)
    def mulcomb(self,n,*rs):#n!/(r1!*r2!*r3!*...)
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:#全方位木
    def __init__(self,N,edge):#単位元self.unitとモノイドdef funcを設定すること,
        #dics[親][根（親の隣接点)]=その部分木での値
        self.unit=(1,0)
        self.mod=10**9+7
        self.edge=edge
        self.cb=comb(N)
        self.fact=self.cb.fact
        self.ifact=self.cb.ifact
        self.par=[-1]*N
        self.N=N
        self.visited=[0]*N
        self.dics=[dict() for _ in range(N)]
        self.ikigake=[]
        self.tot=[self.unit]*N
    
    #@lru_cache(maxsize = None)
    def func(self,x,y):
        #ifact=self.ifact
        #mod=self.mod
        p1,s1=x
        p2,s2=y
        ans=(p1*p2)%self.mod
        ssum=s1+s2
        ans*=self.cb.comb(ssum,s1)
        #ans*=(self.fact[ssum]*self.ifact[s1])%self.mod*self.ifact[s2]%self.mod
        ans%=self.mod
        return ans,ssum 

    def addnode(self,x):#部分木に親のノードを結合する処理,dfsとforwardに出現
        return x[0],x[1]+1

    def _dfs(self,e,pa):
        edge=self.edge
        self.par[e]=pa
        self.ikigake.append(e)
        ans=self.unit
        for ne in edge[e]:
            if self.par[ne]!=-1:
                continue
            ans=self.func(ans,self.addnode(self._dfs(ne,e)))
            #print(ans)
        if pa!=e:
            self.dics[pa][e]=ans
        
        return ans
    
    def forward(self,start):
        self._dfs(start,start)
        #print(t2-t1)
        #count=0
        for e in self.ikigake:
            pa=self.par[e]
            de=self.dics[e]
            nes=tuple(de.keys())
            nvals=tuple(de.values())
            l=len(nes)
            aleft=[self.unit]
            aright=[self.unit]
            cleft=self.unit
            cright=self.unit
            for i in range(l-1):
                aleft.append(self.func(aleft[-1],self.addnode(nvals[i])))
                aright.append(self.func(aright[-1],self.addnode(nvals[-i-1])))
                #count+=4
            self.tot[e]=self.func(aright[-1],self.addnode(nvals[0]))
            for i,ne in enumerate(nes):
                if ne==pa:
                    continue
                self.dics[ne][e]=self.func(aleft[i],aright[-1-i])
                #count+=1
        #print(t3-t2)

def main():
    mod = 1000000007
    #w.sort(key=itemgetter(1),reversed=True)  #二個目の要素で降順並び替え

    N = int(input())
    #N, K = map(int, input().split())
    #A = tuple(map(int, input().split())) #1行ベクトル
    #L = tuple(int(input()) for i in range(N)) #改行ベクトル
    #S = tuple(tuple(map(int, input().split())) for i in range(N)) #改行行列

    def tree_init(N):
        edgelist = [[] for _ in range(N)]
        elist=set()
        for a, b in [map(int, input().split()) for i in range(N-1)]:#木じゃない場合N-1をNに変える
            edgelist[a-1].append(b-1)#ノードの番号が0から始まる場合-1を消す
            edgelist[b-1].append(a-1)
            elist.add((a-1,b-1))
        return edgelist,elist

    edge,elist=tree_init(N)
    cb=comb(N)
    rt=rerooting(N,edge)
    rt.forward(0)

    for a in range(N):
        print(rt.tot[a][0])

if __name__ == "__main__":
    main()

#%%

Submission status: Accepted

Solution code:
#%%
import sys
sys.setrecursionlimit(10**7) #再帰関数の上限,10**5以上の場合python
import math

#heapify(q),heappush(q,a),heappop(q) #q=heapify(q)としないこと、返り値はNone
#import fractions#古いatcoderコンテストの場合GCDなどはここからimportする
from functools import lru_cache#pypyでもうごく
#@lru_cache(maxsize = None)#maxsizeは保存するデータ数の最大値、2**nが最も高効率


def input(): return sys.stdin.readline()[:-1]
def printl(li): _=print(*li, sep="\n") if li else None
def argsort(s, return_sorted=False): 
    inds=sorted(range(len(s)), key=lambda k: s[k])
    if return_sorted: return inds, [s[i] for i in inds]
    return inds
def alp2num(c,cap=False): return ord(c)-97 if not cap else ord(c)-65
def num2alp(i,cap=False): return chr(i+97) if not cap else chr(i+65)
def matmat(A,B):
    K,N,M=len(B),len(A),len(B[0])
    return [[sum([(A[i][k]*B[k][j]) for k in range(K)]) for j in range(M)] for i in range(N)]
def matvec(M,v):
    N,size=len(v),len(M)
    return [sum([M[i][j]*v[j] for j in range(N)]) for i in range(size)]
def T(M):
    n,m=len(M),len(M[0])
    return [[M[j][i] for j in range(n)] for i in range(m)]

        
class comb:
    def __init__(self,N,mod=10**9+7):#コンビネーションnCrをmodで求める、Nは最大のn 
        self.mod=mod
        self.fact=[0]*(N+1)
        self.ifact=[0]*(N+1)
        fact,ifact=self.fact,self.ifact
        fact[0],fact[1],ifact[0],ifact[1]=1,1,1,1
        for i in range(2,N+1):
            x=(fact[i-1]*i)%mod
            fact[i]=x
            ifact[i]=self.extgcd1(x,mod)
        

    @lru_cache(maxsize = None)
    def extgcd1(self,a0,b0):#計算量log(b0),フェルマーの小定理より早い
        u,v,a,b=1,0,a0,b0
        while b:
            t,a=divmod(a,b)
            a,b,u,v=b,a,v,u-t*v
        if a!=1: 
            print("not 素")
            return -1
        return u%b0

    #@lru_cache(maxsize = None)
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    @lru_cache(maxsize = None)
    def mulcomb(self,n,*rs):#n!/(r1!*r2!*r3!*...)
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:#全方位木
    def __init__(self,N,edge):#単位元self.unitとモノイドdef funcを設定すること,
        #dics[親][根（親の隣接点)]=その部分木での値
        self.unit=(1,0)
        self.mod=10**9+7
        self.edge=edge
        self.cb=comb(N)
        self.fact=self.cb.fact
        self.ifact=self.cb.ifact
        self.par=[-1]*N
        self.N=N
        self.visited=[0]*N
        self.dics=[dict() for _ in range(N)]
        self.ikigake=[]
        self.tot=[self.unit]*N
    
    #@lru_cache(maxsize = None)
    def func(self,x,y):
        #ifact=self.ifact
        #mod=self.mod
        p1,s1=x
        p2,s2=y
        ans=(p1*p2)%self.mod
        ssum=s1+s2
        ans*=self.cb.comb(ssum,s1)
        #ans*=(self.fact[ssum]*self.ifact[s1])%self.mod*self.ifact[s2]%self.mod
        ans%=self.mod
        return ans,ssum 

    def addnode(self,x):#部分木に親のノードを結合する処理,dfsとforwardに出現
        return x[0],x[1]+1

    def _dfs(self,e,pa):
        edge=self.edge
        self.par[e]=pa
        self.ikigake.append(e)
        ans=self.unit
        for ne in edge[e]:
            if self.par[ne]!=-1:
                continue
            ans=self.func(ans,self.addnode(self._dfs(ne,e)))
            #print(ans)
        if pa!=e:
            self.dics[pa][e]=ans
        
        return ans
    
    def forward(self,start):
        self._dfs(start,start)
        #print(t2-t1)
        #count=0
        for e in self.ikigake:
            pa=self.par[e]
            de=self.dics[e]
            nes=tuple(de.keys())
            nvals=tuple(de.values())
            l=len(nes)
            aleft=[self.unit]
            aright=[self.unit]
            cleft=self.unit
            cright=self.unit
            for i in range(l-1):
                aleft.append(self.func(aleft[-1],self.addnode(nvals[i])))
                aright.append(self.func(aright[-1],self.addnode(nvals[-i-1])))
                #count+=4
            self.tot[e]=self.func(aright[-1],self.addnode(nvals[0]))
            for i,ne in enumerate(nes):
                if ne==pa:
                    continue
                self.dics[ne][e]=self.func(aleft[i],aright[-1-i])
                #count+=1
        #print(t3-t2)

def main():
    mod = 1000000007
    #w.sort(key=itemgetter(1),reversed=True)  #二個目の要素で降順並び替え

    N = int(input())
    #N, K = map(int, input().split())
    #A = tuple(map(int, input().split())) #1行ベクトル
    #L = tuple(int(input()) for i in range(N)) #改行ベクトル
    #S = tuple(tuple(map(int, input().split())) for i in range(N)) #改行行列

    def tree_init(N):
        edgelist = [[] for _ in range(N)]
        elist=set()
        for a, b in [map(int, input().split()) for i in range(N-1)]:#木じゃない場合N-1をNに変える
            edgelist[a-1].append(b-1)#ノードの番号が0から始まる場合-1を消す
            edgelist[b-1].append(a-1)
            elist.add((a-1,b-1))
        return edgelist,elist

    edge,elist=tree_init(N)
    cb=comb(N)
    rt=rerooting(N,edge)
    rt.forward(0)

    for a in range(N):
        print(rt.tot[a][0])

if __name__ == "__main__":
    main()

#%%

Submission status: Accepted

Solution code:
#%%
import sys
sys.setrecursionlimit(10**7) #再帰関数の上限,10**5以上の場合python
import math

#heapify(q),heappush(q,a),heappop(q) #q=heapify(q)としないこと、返り値はNone
#import fractions#古いatcoderコンテストの場合GCDなどはここからimportする
from functools import lru_cache#pypyでもうごく
#@lru_cache(maxsize = None)#maxsizeは保存するデータ数の最大値、2**nが最も高効率


def input(): return sys.stdin.readline()[:-1]
def printl(li): _=print(*li, sep="\n") if li else None
def argsort(s, return_sorted=False): 
    inds=sorted(range(len(s)), key=lambda k: s[k])
    if return_sorted: return inds, [s[i] for i in inds]
    return inds
def alp2num(c,cap=False): return ord(c)-97 if not cap else ord(c)-65
def num2alp(i,cap=False): return chr(i+97) if not cap else chr(i+65)
def matmat(A,B):
    K,N,M=len(B),len(A),len(B[0])
    return [[sum([(A[i][k]*B[k][j]) for k in range(K)]) for j in range(M)] for i in range(N)]
def matvec(M,v):
    N,size=len(v),len(M)
    return [sum([M[i][j]*v[j] for j in range(N)]) for i in range(size)]
def T(M):
    n,m=len(M),len(M[0])
    return [[M[j][i] for j in range(n)] for i in range(m)]

        
class comb:
    def __init__(self,N,mod=10**9+7):#コンビネーションnCrをmodで求める、Nは最大のn 
        self.mod=mod
        self.fact=[0]*(N+1)
        self.ifact=[0]*(N+1)
        fact,ifact=self.fact,self.ifact
        fact[0],fact[1],ifact[0],ifact[1]=1,1,1,1
        for i in range(2,N+1):
            x=(fact[i-1]*i)%mod
            fact[i]=x
            ifact[i]=self.extgcd1(x,mod)
        

    @lru_cache(maxsize = None)
    def extgcd1(self,a0,b0):#計算量log(b0),フェルマーの小定理より早い
        u,v,a,b=1,0,a0,b0
        while b:
            t,a=divmod(a,b)
            a,b,u,v=b,a,v,u-t*v
        if a!=1: 
            print("not 素")
            return -1
        return u%b0

    @lru_cache(maxsize = None)
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    @lru_cache(maxsize = None)
    def mulcomb(self,n,*rs):#n!/(r1!*r2!*r3!*...)
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:#全方位木
    def __init__(self,N,edge):#単位元self.unitとモノイドdef funcを設定すること,
        #dics[親][根（親の隣接点)]=その部分木での値
        self.unit=(1,0)
        self.mod=10**9+7
        self.edge=edge
        cb=comb(N)
        self.fact=cb.fact
        self.ifact=cb.ifact
        self.par=[-1]*N
        self.N=N
        self.visited=[0]*N
        self.dics=[dict() for _ in range(N)]
        self.ikigake=[]
        self.tot=[self.unit]*N
    
    #@lru_cache(maxsize = None)
    def func(self,x,y):
        #ifact=self.ifact
        #mod=self.mod
        p1,s1=x
        p2,s2=y
        ans=(p1*p2)%self.mod
        ssum=s1+s2
        ans*=(self.fact[ssum]*self.ifact[s1])%self.mod*self.ifact[s2]%self.mod
        ans%=self.mod
        return ans,ssum 

    def addnode(self,x):#部分木に親のノードを結合する処理,dfsとforwardに出現
        return x[0],x[1]+1

    def _dfs(self,e,pa):
        edge=self.edge
        self.par[e]=pa
        self.ikigake.append(e)
        ans=self.unit
        for ne in edge[e]:
            if self.par[ne]!=-1:
                continue
            ans=self.func(ans,self.addnode(self._dfs(ne,e)))
            #print(ans)
        if pa!=e:
            self.dics[pa][e]=ans
        
        return ans
    
    def forward(self,start):
        self._dfs(start,start)
        #print(t2-t1)
        #count=0
        for e in self.ikigake:
            pa=self.par[e]
            de=self.dics[e]
            nes=tuple(de.keys())
            nvals=tuple(de.values())
            l=len(nes)
            aleft=[self.unit]
            aright=[self.unit]
            cleft=self.unit
            cright=self.unit
            for i in range(l-1):
                aleft.append(self.func(aleft[-1],self.addnode(nvals[i])))
                aright.append(self.func(aright[-1],self.addnode(nvals[-i-1])))
                #count+=4
            self.tot[e]=self.func(aright[-1],self.addnode(nvals[0]))
            for i,ne in enumerate(nes):
                if ne==pa:
                    continue
                self.dics[ne][e]=self.func(aleft[i],aright[-1-i])
                #count+=1
        #print(t3-t2)

def main():
    mod = 1000000007
    #w.sort(key=itemgetter(1),reversed=True)  #二個目の要素で降順並び替え

    N = int(input())
    #N, K = map(int, input().split())
    #A = tuple(map(int, input().split())) #1行ベクトル
    #L = tuple(int(input()) for i in range(N)) #改行ベクトル
    #S = tuple(tuple(map(int, input().split())) for i in range(N)) #改行行列

    def tree_init(N):
        edgelist = [[] for _ in range(N)]
        elist=set()
        for a, b in [map(int, input().split()) for i in range(N-1)]:#木じゃない場合N-1をNに変える
            edgelist[a-1].append(b-1)#ノードの番号が0から始まる場合-1を消す
            edgelist[b-1].append(a-1)
            elist.add((a-1,b-1))
        return edgelist,elist

    edge,elist=tree_init(N)
    cb=comb(N)
    rt=rerooting(N,edge)
    rt.forward(0)

    for a in range(N):
        print(rt.tot[a][0])

if __name__ == "__main__":
    main()

#%%

Submission status: Accepted

Solution code:
#%%
import sys
sys.setrecursionlimit(10**7) #再帰関数の上限,10**5以上の場合python
import math

#heapify(q),heappush(q,a),heappop(q) #q=heapify(q)としないこと、返り値はNone
#import fractions#古いatcoderコンテストの場合GCDなどはここからimportする
from functools import lru_cache#pypyでもうごく
#@lru_cache(maxsize = None)#maxsizeは保存するデータ数の最大値、2**nが最も高効率


def input(): return sys.stdin.readline()[:-1]
def printl(li): _=print(*li, sep="\n") if li else None
def argsort(s, return_sorted=False): 
    inds=sorted(range(len(s)), key=lambda k: s[k])
    if return_sorted: return inds, [s[i] for i in inds]
    return inds
def alp2num(c,cap=False): return ord(c)-97 if not cap else ord(c)-65
def num2alp(i,cap=False): return chr(i+97) if not cap else chr(i+65)
def matmat(A,B):
    K,N,M=len(B),len(A),len(B[0])
    return [[sum([(A[i][k]*B[k][j]) for k in range(K)]) for j in range(M)] for i in range(N)]
def matvec(M,v):
    N,size=len(v),len(M)
    return [sum([M[i][j]*v[j] for j in range(N)]) for i in range(size)]
def T(M):
    n,m=len(M),len(M[0])
    return [[M[j][i] for j in range(n)] for i in range(m)]

        
class comb:
    def __init__(self,N,mod=10**9+7):#コンビネーションnCrをmodで求める、Nは最大のn 
        self.mod=mod
        self.fact=[0]*(N+1)
        self.ifact=[0]*(N+1)
        fact,ifact=self.fact,self.ifact
        fact[0],fact[1],ifact[0],ifact[1]=1,1,1,1
        for i in range(2,N+1):
            x=(fact[i-1]*i)%mod
            fact[i]=x
            ifact[i]=self.extgcd1(x,mod)
        

    @lru_cache(maxsize = None)
    def extgcd1(self,a0,b0):#計算量log(b0),フェルマーの小定理より早い
        u,v,a,b=1,0,a0,b0
        while b:
            t,a=divmod(a,b)
            a,b,u,v=b,a,v,u-t*v
        if a!=1: 
            print("not 素")
            return -1
        return u%b0

    @lru_cache(maxsize = None)
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    @lru_cache(maxsize = None)
    def mulcomb(self,n,*rs):#n!/(r1!*r2!*r3!*...)
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:#全方位木
    def __init__(self,N,edge):#単位元self.unitとモノイドdef funcを設定すること,
        #dics[親][根（親の隣接点)]=その部分木での値
        self.unit=(1,0)
        self.mod=10**9+7
        self.edge=edge
        cb=comb(N)
        self.fact=cb.fact
        self.ifact=cb.ifact
        self.par=[-1]*N
        self.N=N
        self.visited=[0]*N
        self.dics=[dict() for _ in range(N)]
        self.ikigake=[]
        self.tot=[self.unit]*N
    
    #@lru_cache(maxsize = None)
    def func(self,x,y):
        ifact=self.ifact
        mod=self.mod
        p1,s1=x
        p2,s2=y
        ans=(p1*p2)%mod
        ssum=s1+s2
        #print(x,y,slist)
        ans*=(self.fact[ssum]*ifact[s1])%mod*ifact[s2]%mod
        ans%=mod
        return ans,ssum 

    def addnode(self,x):#部分木に親のノードを結合する処理,dfsとforwardに出現
        return x[0],x[1]+1

    def _dfs(self,e,pa):
        edge=self.edge
        self.par[e]=pa
        self.ikigake.append(e)
        ans=self.unit
        for ne in edge[e]:
            if self.par[ne]!=-1:
                continue
            ans=self.func(ans,self.addnode(self._dfs(ne,e)))
            #print(ans)
        if pa!=e:
            self.dics[pa][e]=ans
        
        return ans
    
    def forward(self,start):
        self._dfs(start,start)
        #print(t2-t1)
        #count=0
        for e in self.ikigake:
            pa=self.par[e]
            de=self.dics[e]
            nes=tuple(de.keys())
            nvals=tuple(de.values())
            l=len(nes)
            aleft=[self.unit]
            aright=[self.unit]
            cleft=self.unit
            cright=self.unit
            for i in range(l-1):
                aleft.append(self.func(aleft[-1],self.addnode(nvals[i])))
                aright.append(self.func(aright[-1],self.addnode(nvals[-i-1])))
                #count+=4
            self.tot[e]=self.func(aright[-1],self.addnode(nvals[0]))
            for i,ne in enumerate(nes):
                if ne==pa:
                    continue
                self.dics[ne][e]=self.func(aleft[i],aright[-1-i])
                #count+=1
        #print(t3-t2)

def main():
    mod = 1000000007
    #w.sort(key=itemgetter(1),reversed=True)  #二個目の要素で降順並び替え

    N = int(input())
    #N, K = map(int, input().split())
    #A = tuple(map(int, input().split())) #1行ベクトル
    #L = tuple(int(input()) for i in range(N)) #改行ベクトル
    #S = tuple(tuple(map(int, input().split())) for i in range(N)) #改行行列

    def tree_init(N):
        edgelist = [[] for _ in range(N)]
        elist=set()
        for a, b in [map(int, input().split()) for i in range(N-1)]:#木じゃない場合N-1をNに変える
            edgelist[a-1].append(b-1)#ノードの番号が0から始まる場合-1を消す
            edgelist[b-1].append(a-1)
            elist.add((a-1,b-1))
        return edgelist,elist

    edge,elist=tree_init(N)
    cb=comb(N)
    rt=rerooting(N,edge)
    rt.forward(0)

    for a in range(N):
        print(rt.tot[a][0])

if __name__ == "__main__":
    main()

#%%

Submission status: Accepted

Solution code:
# 全方位木DP
# トポロジカルソート→木DP→全方位
from collections import deque
import sys

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

n = int(readline())

# modの会場が必要なのでライブラリから
mod = 10 ** 9 + 7
N = n + 5
bikkuri = [0 for i in range(N)]
bikkuri[0] = 1
gyaku = [0 for i in range(N)]
gyaku[0] = 1
for i in range(1, N):
    bikkuri[i] = (i * bikkuri[i - 1]) % mod
    gyaku[i] = pow(bikkuri[i], mod - 2, mod)

graph = [[] for _ in range(n + 1)]
m = map(int, read().split())
AB = zip(m, m)
for a, b in AB:
    graph[a].append(b)
    graph[b].append(a)

# topological sort
par = [-1] * (n + 1)
que = deque([])
que.append(1)
topo = []
while que:
    v = que.popleft()
    topo.append(v)
    for u in graph[v]:
        if u == par[v]:
            continue
        par[u] = v
        graph[u].remove(v)
        que.append(u)

# これでparのリストとtopological_sortと子供方向のみグラフを得る
# 木DP
dp1 = [0] * (n + 1)
size = [0] * (n + 1)
edge_index = [{} for _ in range(n + 1)]
dpl = [[] for _ in range(n + 1)]
dpr = [[] for _ in range(n + 1)]
for v in topo[::-1]:
    dp1[v] = 1
    size[v] = 1
    # サイズを先に計算
    for u in graph[v]:
        size[v] += size[u]
        dp1[v] *= dp1[u]
        dp1[v] *= gyaku[size[u]]
    # 次に組み合わせを考える
    # 左から
    temp = 1
    for i in range(len(graph[v])):
        u = graph[v][i]
        edge_index[v][u] = i
        temp *= dp1[u]
        temp %= mod
        temp *= gyaku[size[u]]
        temp %= mod
        dpl[v].append(temp)
    # 右から
    temp = 1
    for i in range(len(graph[v]))[::-1]:
        u = graph[v][i]
        temp *= dp1[u]
        temp *= gyaku[size[u]]
        temp %= mod
        dpr[v].append(temp)
    dp1[v] *= bikkuri[size[v] - 1]
    dp1[v] %= mod

# 全方位
ans = [0] * (n + 1)
dp2 = [0] * (n + 1)

for v in topo:
    # 根の時
    if par[v] == -1:
        dp2[v] = 1
        ans[v] = dp1[v]
    else:
        # 上側の処理
        dp2[v] = 1
        p = par[v]
        # 上からみたv以外の累積積を取りたい。
        # graph[p]において、vは何番目かを考える。
        v_idx = edge_index[p][v]
        dp2[v] *= dp2[p] * gyaku[n - size[p]]
        dp2[v] *= bikkuri[n - size[v] - 1]
        dp2[v] %= mod
        # 左からv_idx個, idxはv_idx-1まで
        if dpl[p]:
            if v_idx - 1 >= 0:
                dp2[v] *= dpl[p][v_idx - 1]
                dp2[v] %= mod
            # 右からlen(grap[v])-(v_idx+1)個→idxはlen(graph[v])-v_idx-2
            if v_idx < len(graph[p]) - 1:
                dp2[v] *= dpr[p][len(graph[p]) - 2 - v_idx]
                dp2[v] %= mod
    # 上側と下側の合体
    ans[v] = bikkuri[n - 1]
    if dpl[v]:
        ans[v] *= dpl[v][-1]
    ans[v] *= dp2[v] * gyaku[n - size[v]]
    ans[v] %= mod

for i in range(1, n + 1):
    print(ans[i])