Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
ab=[list(map(int,input().split())) for _ in range(n-1)]
mod=pow(10,9)+7
ki=[[] for _ in range(n)]
todo=[]
for a,b in ab:
  ki[a-1].append(b-1)
  ki[b-1].append(a-1)
import sys
sys.setrecursionlimit(100000)
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod
g1 = [1, 1] 
g2 = [1, 1] 
inverse = [0, 1]
for i in range( 2, n + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )
memo={}
def dfs(i,pare):#根がi、親がpareの部分木についての値を返す。[サイズ,整数の書き方の場合の数]
  if (i,pare) in memo:
    return memo[(i,pare)]
  l=ki[i]
  ret=0
  sizes=[]
  pats=[]
  sum_size=0
  ret=1
  for li in l:
    if li==pare:
      continue
    size,pat=dfs(li,i)
    sizes.append(size)
    sum_size+=size
    ret*=cmb(sum_size,size,mod)
    ret*=pat
  memo[(i,pare)]=(sum_size+1,ret)
  return (sum_size+1,ret)
for i in range(n):
  print(dfs(i,-1)[1])

Fixed submission:
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
def main():
    n=int(input())
    def cmb(n, r, mod):
        if ( r<0 or r>n ):
            return 0
        r = min(r, n-r)
        return g1[n] * g2[r] * g2[n-r] % mod
    mod = 10**9+7 #出力の制限
    g1 = [1, 1] # 元テーブル
    g2 = [1, 1] #逆元テーブル
    inverse = [0, 1] #逆元テーブル計算用テーブル
    for i in range( 2, n + 1 ):
        g1.append( ( g1[-1] * i ) % mod )
        inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
        g2.append( (g2[-1] * inverse[-1]) % mod )

    ki=[[] for _ in range(n)]
    for _ in range(n-1):
        a,b=map(int,input().split())
        a,b=a-1,b-1
        ki[a].append(b)
        ki[b].append(a)
    memo={} # memo[(p,v)]:p->vの部分木のサイズ、整数の書き方
    def dfs(p,v):
        if (p,v) in memo:return memo[(p,v)]
        size,pat=0,1
        tmps,tmpp=1,1
        deg=len(ki[v])
        for nv in ki[v]:
            if nv==p:continue
            si,pi=dfs(v,nv)
            size+=si
            tmps*=g2[si]
            tmps%=mod
            tmpp*=pi
            tmpp%=mod
        pat=(g1[size]*tmps*tmpp)%mod
        memo[(p,v)]=(size+1,pat)
        return (size+1,pat)
    ans=[0]*n
    def bfs(p,v,res):
        if p!=-1:memo[(v,p)]=res
        deg=len(ki[v])
        tmps,tmpp=1,1
        for i in range(deg):
            si,pi=memo[(v,ki[v][i])]
            tmps*=g2[si]
            tmpp*=pi
            tmps%=mod
            tmpp%=mod

        ans[v]=g1[n-1]*tmps*tmpp
        ans[v]%=mod

        dpl=[1]*(deg+1)
        dpr=[1]*(deg+1)
        tmp=1
        for i in range(deg):
            si,pi=memo[(v,ki[v][i])]
            tmp*=pi*g2[si]
            tmp%=mod
            dpl[i+1]=tmp
        tmp=1
        for i in range(deg-1,-1,-1):
            si,pi=memo[(v,ki[v][i])]
            tmp*=pi*g2[si]
            tmp%=mod
            dpr[i]=tmp
        for i in range(deg):
            nv=ki[v][i]
            if p==nv:continue
            bfs(v,nv,(n-memo[(v,nv)][0],(g1[n-1-memo[(v,nv)][0]]*dpl[i]*dpr[i+1])%mod))
    dfs(-1,0)
    #print(memo)
    bfs(-1,0,0)
    print(*ans,sep='\n')
    #print(memo)

if __name__=='__main__':
    main()

Buggy python submission (verdict: Runtime Error):
n=int(input())
ab=[list(map(int,input().split())) for _ in range(n-1)]
mod=pow(10,9)+7
ki=[[] for _ in range(n)]
todo=[]
for a,b in ab:
  ki[a-1].append(b-1)
  ki[b-1].append(a-1)
  todo.append((a-1,b-1))
  todo.append((b-1,a-1))
import sys
sys.setrecursionlimit(100000)
nCr = {}
def cmb(n, r):
    if r == 0 or r == n: return 1
    if r == 1: return n
    if (n,r) in nCr: return nCr[(n,r)]
    nCr[(n,r)] = cmb(n-1,r) + cmb(n-1,r-1)
    return nCr[(n,r)]%mod

dp=[[0]*n for _ in range(n)]
def node(i,j):
  if dp[i][j]!=0:
    return dp[i][j]
  l=ki[j]
  pat,size=1,0
  for li in l:
    if li!=i:
      if dp[j][li]!=0:
        sizei,pati=dp[j][li]
      else:
        sizei,pati=node(j,li)
        sizei,pati=sizei%mod,pati%mod
        dp[j][li]=(sizei,pati)
      size+=sizei
      size%=mod
      pat*=cmb(size,sizei)
      pat*=pati
      pat%=mod
  return size+1,pat
while todo:
    t=todo.pop()
    if dp[t[0]][t[1]]==0:
        size,pat=node(t[0],t[1])
        dp[t[0]][t[1]]=(size,pat)

for i in range(n):
  l=ki[i]
  size=0
  pat=1
  for li in l:
    sizei,pati=dp[i][li]
    size+=sizei
    pat*=cmb(size,sizei)
    pat*=pati
    pat%=mod
  print(pat)

Fixed submission:
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
def main():
    n=int(input())
    def cmb(n, r, mod):
        if ( r<0 or r>n ):
            return 0
        r = min(r, n-r)
        return g1[n] * g2[r] * g2[n-r] % mod
    mod = 10**9+7 #出力の制限
    g1 = [1, 1] # 元テーブル
    g2 = [1, 1] #逆元テーブル
    inverse = [0, 1] #逆元テーブル計算用テーブル
    for i in range( 2, n + 1 ):
        g1.append( ( g1[-1] * i ) % mod )
        inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
        g2.append( (g2[-1] * inverse[-1]) % mod )

    ki=[[] for _ in range(n)]
    for _ in range(n-1):
        a,b=map(int,input().split())
        a,b=a-1,b-1
        ki[a].append(b)
        ki[b].append(a)
    memo={} # memo[(p,v)]:p->vの部分木のサイズ、整数の書き方
    def dfs(p,v):
        if (p,v) in memo:return memo[(p,v)]
        size,pat=0,1
        tmps,tmpp=1,1
        deg=len(ki[v])
        for nv in ki[v]:
            if nv==p:continue
            si,pi=dfs(v,nv)
            size+=si
            tmps*=g2[si]
            tmps%=mod
            tmpp*=pi
            tmpp%=mod
        pat=(g1[size]*tmps*tmpp)%mod
        memo[(p,v)]=(size+1,pat)
        return (size+1,pat)
    ans=[0]*n
    def bfs(p,v,res):
        if p!=-1:memo[(v,p)]=res
        deg=len(ki[v])
        tmps,tmpp=1,1
        for i in range(deg):
            si,pi=memo[(v,ki[v][i])]
            tmps*=g2[si]
            tmpp*=pi
            tmps%=mod
            tmpp%=mod

        ans[v]=g1[n-1]*tmps*tmpp
        ans[v]%=mod

        dpl=[1]*(deg+1)
        dpr=[1]*(deg+1)
        tmp=1
        for i in range(deg):
            si,pi=memo[(v,ki[v][i])]
            tmp*=pi*g2[si]
            tmp%=mod
            dpl[i+1]=tmp
        tmp=1
        for i in range(deg-1,-1,-1):
            si,pi=memo[(v,ki[v][i])]
            tmp*=pi*g2[si]
            tmp%=mod
            dpr[i]=tmp
        for i in range(deg):
            nv=ki[v][i]
            if p==nv:continue
            bfs(v,nv,(n-memo[(v,nv)][0],(g1[n-1-memo[(v,nv)][0]]*dpl[i]*dpr[i+1])%mod))
    dfs(-1,0)
    #print(memo)
    bfs(-1,0,0)
    print(*ans,sep='\n')
    #print(memo)

if __name__=='__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
ab=[list(map(int,input().split())) for _ in range(n-1)]
mod=pow(10,9)+7
ki=[[] for _ in range(n)]
todo=[]
for a,b in ab:
  ki[a-1].append(b-1)
  ki[b-1].append(a-1)
  todo.append((a-1,b-1))
  todo.append((b-1,a-1))
import sys
sys.setrecursionlimit(100000)
nCr = {}
def cmb(n, r):
    if r == 0 or r == n: return 1
    if r == 1: return n
    if (n,r) in nCr: return nCr[(n,r)]
    nCr[(n,r)] = cmb(n-1,r) + cmb(n-1,r-1)
    return nCr[(n,r)]%mod

dp={}
def node(i,j):
  if (i,j) in dp:
    return dp[(i,j)]
  l=ki[j]
  pat,size=1,0
  for li in l:
    if li!=i:
      if (j,li) in dp:
        sizei,pati=dp[(j,li)]
      else:
        sizei,pati=node(j,li)
        dp[(j,li)]=(sizei,pati)
      size+=sizei
      pat*=cmb(size,sizei)
      pat*=pati
      pat%=mod
  return size+1,pat
while len(dp)<2*(n-1):
    t=todo.pop()
    if t not in dp:
        size,pat=node(t[0],t[1])
        dp[t]=size,pat

for i in range(n):
  l=ki[i]
  size=0
  pat=1
  for li in l:
    sizei,pati=dp[(i,li)]
    size+=sizei
    pat*=cmb(size,sizei)
    pat*=pati
    pat%=mod
  print(pat)

Fixed submission:
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
def main():
    n=int(input())
    def cmb(n, r, mod):
        if ( r<0 or r>n ):
            return 0
        r = min(r, n-r)
        return g1[n] * g2[r] * g2[n-r] % mod
    mod = 10**9+7 #出力の制限
    g1 = [1, 1] # 元テーブル
    g2 = [1, 1] #逆元テーブル
    inverse = [0, 1] #逆元テーブル計算用テーブル
    for i in range( 2, n + 1 ):
        g1.append( ( g1[-1] * i ) % mod )
        inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
        g2.append( (g2[-1] * inverse[-1]) % mod )

    ki=[[] for _ in range(n)]
    for _ in range(n-1):
        a,b=map(int,input().split())
        a,b=a-1,b-1
        ki[a].append(b)
        ki[b].append(a)
    memo={} # memo[(p,v)]:p->vの部分木のサイズ、整数の書き方
    def dfs(p,v):
        if (p,v) in memo:return memo[(p,v)]
        size,pat=0,1
        tmps,tmpp=1,1
        deg=len(ki[v])
        for nv in ki[v]:
            if nv==p:continue
            si,pi=dfs(v,nv)
            size+=si
            tmps*=g2[si]
            tmps%=mod
            tmpp*=pi
            tmpp%=mod
        pat=(g1[size]*tmps*tmpp)%mod
        memo[(p,v)]=(size+1,pat)
        return (size+1,pat)
    ans=[0]*n
    def bfs(p,v,res):
        if p!=-1:memo[(v,p)]=res
        deg=len(ki[v])
        tmps,tmpp=1,1
        for i in range(deg):
            si,pi=memo[(v,ki[v][i])]
            tmps*=g2[si]
            tmpp*=pi
            tmps%=mod
            tmpp%=mod

        ans[v]=g1[n-1]*tmps*tmpp
        ans[v]%=mod

        dpl=[1]*(deg+1)
        dpr=[1]*(deg+1)
        tmp=1
        for i in range(deg):
            si,pi=memo[(v,ki[v][i])]
            tmp*=pi*g2[si]
            tmp%=mod
            dpl[i+1]=tmp
        tmp=1
        for i in range(deg-1,-1,-1):
            si,pi=memo[(v,ki[v][i])]
            tmp*=pi*g2[si]
            tmp%=mod
            dpr[i]=tmp
        for i in range(deg):
            nv=ki[v][i]
            if p==nv:continue
            bfs(v,nv,(n-memo[(v,nv)][0],(g1[n-1-memo[(v,nv)][0]]*dpl[i]*dpr[i+1])%mod))
    dfs(-1,0)
    #print(memo)
    bfs(-1,0,0)
    print(*ans,sep='\n')
    #print(memo)

if __name__=='__main__':
    main()