Problem:
 Score : 600 points    Problem Statement  We have a tree with N vertices numbered 1 to N . The i -th edge in this tree connects Vertex a_i and b_i .
For each k=1, ..., N , solve the problem below:   Consider writing a number on each vertex in the tree in the following manner:  First, write 1 on Vertex k .  Then, for each of the numbers 2, ..., N in this order, write the number on the vertex chosen as follows:  Choose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.      Find the number of ways in which we can write the numbers on the vertices, modulo (10^9+7) .       Constraints   2 \leq N \leq 2 \times 10^5  1 \leq a_i,b_i \leq N  The given graph is a tree.         Input  Input is given from Standard Input in the following format:  N  a_1  b_1  :  a_{N-1}  b_{N-1}       Output  For each k=1, 2, ..., N in this order, print a line containing the answer to the problem.        Sample Input 1 3
1 2
1 3      Sample Output 1 2
1
1  The graph in this input is as follows:   For k=1 , there are two ways in which we can write the numbers on the vertices, as follows:   Writing 1, 2, 3 on Vertex 1, 2, 3 , respectively  Writing 1, 3, 2 on Vertex 1, 2, 3 , respectively        Sample Input 2 2
1 2      Sample Output 2 1
1  The graph in this input is as follows:        Sample Input 3 5
1 2
2 3
3 4
3 5      Sample Output 3 2
8
12
3
3  The graph in this input is as follows:        Sample Input 4 8
1 2
2 3
3 4
3 5
3 6
6 7
6 8      Sample Output 4 40
280
840
120
120
504
72
72  The graph in this input is as follows:

Solution (Python):

import sys
sys.setrecursionlimit(10**7) 
import math
from collections import deque 


from functools import lru_cache



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:
    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)%self.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):
        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)
        

    
    def extgcd1(self,a0,b0):
        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

    
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    
    def mulcomb(self,n,*rs):
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:
    def __init__(self,N,edge):
        
        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
    
    
    def func(self,x,y):
        
        
        p1,s1=x
        p2,s2=y
        ans=modint(p1*p2)
        ssum=s1+s2
        ans*=self.cb.comb(ssum,s1)
        
        
        return ans,ssum 

    def addnode(self,x):
        return x[0],x[1]+1

    
    
    
    
    
    
    
    
    
    
    
    
        
    
    def _dfs(self,start):
        edge=self.edge
        N=self.N
        par=self.par
        q=deque([(start,start)])
        while len(q):
            e,pa=q.pop()
            if par[e]!=-1:continue
            par[e]=pa
            self.ikigake.append(e)
            for ne in edge[e]:q.append((ne,e))
        
        for e in reversed(self.ikigake[1:]):
            pa=par[e]
            ans=self.unit
            de=self.dics[e]
            for val in de.values():
                ans=self.func(ans,val)
            self.dics[pa][e]=self.addnode(ans)

    def forward(self,start):
        self._dfs(start)
        
        
        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],nvals[i]))
                aright.append(self.func(aright[-1],nvals[-i-1]))
                
            
            self.tot[e]=self.func(aright[-1],nvals[0])
            for i,ne in enumerate(nes):
                if ne==pa:
                    continue
                self.dics[ne][e]=self.addnode(self.func(aleft[i],aright[-1-i]))
                
        

def main():
    mod = 1000000007
    

    N = int(input())
    
    
    
    

    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)]:
            edgelist[a-1].append(b-1)
            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()

Solution (Python):

import sys
sys.setrecursionlimit(10**7) 
import math
from collections import deque 


from functools import lru_cache



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:
    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)%self.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):
        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)
        

    
    def extgcd1(self,a0,b0):
        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

    
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    
    def mulcomb(self,n,*rs):
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:
    def __init__(self,N,edge):
        
        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
    
    
    def func(self,x,y):
        
        
        p1,s1=x
        p2,s2=y
        ans=modint(p1*p2)
        ssum=s1+s2
        ans*=self.cb.comb(ssum,s1)
        
        
        return ans,ssum 

    def addnode(self,x):
        return x[0],x[1]+1

    
    
    
    
    
    
    
    
    
    
    
    
        
    
    def _dfs(self,start):
        edge=self.edge
        N=self.N
        par=self.par
        q=deque([(start,start)])
        while len(q):
            e,pa=q.pop()
            if par[e]!=-1:continue
            par[e]=pa
            self.ikigake.append(e)
            for ne in edge[e]:q.append((ne,e))
        
        for e in reversed(self.ikigake[1:]):
            pa=par[e]
            ans=self.unit
            de=self.dics[e]
            for val in de.values():
                ans=self.func(ans,self.addnode(val))
            self.dics[pa][e]=ans

    def forward(self,start):
        self._dfs(start)
        
        
        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])))
                
            
            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])
                
        

def main():
    mod = 1000000007
    

    N = int(input())
    
    
    
    

    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)]:
            edgelist[a-1].append(b-1)
            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()

Solution (Python):

import sys
sys.setrecursionlimit(10**7) 
import math
from collections import deque 


from functools import lru_cache



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:
    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)%self.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):
        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)
        

    
    def extgcd1(self,a0,b0):
        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

    
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    
    def mulcomb(self,n,*rs):
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:
    def __init__(self,N,edge):
        
        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
    
    
    def func(self,x,y):
        
        
        p1,s1=x
        p2,s2=y
        ans=modint(p1*p2)
        ssum=s1+s2
        ans*=self.cb.comb(ssum,s1)
        
        
        return ans,ssum 

    def addnode(self,x):
        return x[0],x[1]+1

    
    
    
    
    
    
    
    
    
    
    
    
        
    
    def _dfs(self,start):
        edge=self.edge
        N=self.N
        par=self.par
        q=deque([(start,start)])
        while len(q):
            e,pa=q.pop()
            if par[e]!=-1:continue
            par[e]=pa
            self.ikigake.append(e)
            for ne in edge[e]:q.append((ne,e))
        
        for e in reversed(self.ikigake[1:]):
            pa=par[e]
            ans=self.unit
            de=self.dics[e]
            for ne in edge[e]:
                if ne==pa:continue
                ans=self.func(ans,self.addnode(de[ne]))
            self.dics[pa][e]=ans
        
    def forward(self,start):
        self._dfs(start)
        
        
        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])))
                
            
            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])
                
        

def main():
    mod = 1000000007
    

    N = int(input())
    
    
    
    

    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)]:
            edgelist[a-1].append(b-1)
            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()

Solution (Python):

import sys
sys.setrecursionlimit(10**7) 
import math
from collections import deque 


from functools import lru_cache



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:
    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)%self.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):
        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)
        

    
    def extgcd1(self,a0,b0):
        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

    
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    
    def mulcomb(self,n,*rs):
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:
    def __init__(self,N,edge):
        
        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
    
    
    def func(self,x,y):
        
        
        p1,s1=x
        p2,s2=y
        ans=modint(p1*p2)
        ssum=s1+s2
        ans*=self.cb.comb(ssum,s1)
        
        
        return ans,ssum 

    def addnode(self,x):
        return x[0],x[1]+1

    
    
    
    
    
    
    
    
    
    
    
    
        
    
    def _dfs(self,start):
        edge=self.edge
        N=self.N
        par=self.par
        q=deque([(start,start)])
        while len(q):
            e,pa=q.pop()
            if par[e]!=-1:continue
            par[e]=pa
            self.ikigake.append(e)
            for ne in edge[e]:q.append((ne,e))
        
        for e in reversed(self.ikigake):
            pa=par[e]
            if pa==e:continue
            ans=self.unit
            de=self.dics[e]
            for ne in edge[e]:
                if ne==pa:continue
                ans=self.func(ans,self.addnode(de[ne]))
            self.dics[pa][e]=ans
        
    def forward(self,start):
        self._dfs(start)
        
        
        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])))
                
            
            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])
                
        

def main():
    mod = 1000000007
    

    N = int(input())
    
    
    
    

    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)]:
            edgelist[a-1].append(b-1)
            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()

Solution (Python):

import sys
sys.setrecursionlimit(10**7) 
import math



from functools import lru_cache



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:
    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):
        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)
        

    
    def extgcd1(self,a0,b0):
        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

    
    def comb(self,n,r): return (self.fact[n]*self.ifact[r]%self.mod)*self.ifact[n-r]%self.mod

    
    def mulcomb(self,n,*rs):
        ans=self.fact[n]
        for r in rs: ans=(ans*self.ifact[r])%self.mod
        return ans

class rerooting:
    def __init__(self,N,edge):
        
        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
    
    
    def func(self,x,y):
        
        
        p1,s1=x
        p2,s2=y
        ans=modint(p1*p2)
        ssum=s1+s2
        ans*=self.cb.comb(ssum,s1)
        
        
        return ans,ssum 

    def addnode(self,x):
        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)))
            
        if pa!=e:
            self.dics[pa][e]=ans
        
        return ans
    
    def forward(self,start):
        self._dfs(start,start)
        
        
        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])))
                
            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])
                
        

def main():
    mod = 1000000007
    

    N = int(input())
    
    
    
    

    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)]:
            edgelist[a-1].append(b-1)
            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()