Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**9)
class Combination:
  def __init__(self, n_max, mod=10**9+7):
    self.mod = mod
    self.modinv = self.make_modinv_list(n_max)
    self.fac, self.facinv = self.make_factorial_list(n_max)

  def __call__(self, n, r):
    return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod

  def make_factorial_list(self, n):
    # 階乗のリストと階乗のmod逆元のリストを返す O(n)
    # self.make_modinv_list()が先に実行されている必要がある
    fac = [1]
    facinv = [1]
    for i in range(1, n+1):
      fac.append(fac[i-1] * i % self.mod)
      facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
    return fac, facinv

  def make_modinv_list(self, n):
    # 0からnまでのmod逆元のリストを返す O(n)
    modinv = [0] * (n+1)
    modinv[1] = 1
    for i in range(2, n+1):
        modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
    return modinv

N,K = map(int,input().split())
adj = [ [ ]for _ in range(N) ]
comb = Combination(10**5)

def nPr(n,r):
  if n < r: return 0
  return comb(n, r) * comb.fac[r]

for _ in range(N-1):
  a,b = map(int,input().split())
  a -= 1
  b -= 1
  adj[a].append(b)
  adj[b].append(a)

def dfs(v, p=-1):
  global ans
  c = 0
  for nei in adj[v]:
    if nei == p: continue
    c += 1
    dfs(nei, v)

  nk = K-1 if p==-1 else K-2
  ans *= nPr(nk, c)
  ans %= 10**9+7

ans = K
dfs(0)
print(ans)

Fixed submission:
import sys
sys.setrecursionlimit(10**9)
class Combination:
  def __init__(self, n_max, mod=10**9+7):
    self.mod = mod
    self.modinv = self.make_modinv_list(n_max)
    self.fac, self.facinv = self.make_factorial_list(n_max)

  def __call__(self, n, r):
    return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod

  def make_factorial_list(self, n):
    # 階乗のリストと階乗のmod逆元のリストを返す O(n)
    # self.make_modinv_list()が先に実行されている必要がある
    fac = [1]
    facinv = [1]
    for i in range(1, n+1):
      fac.append(fac[i-1] * i % self.mod)
      facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
    return fac, facinv

  def make_modinv_list(self, n):
    # 0からnまでのmod逆元のリストを返す O(n)
    modinv = [0] * (n+1)
    modinv[1] = 1
    for i in range(2, n+1):
        modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
    return modinv

N,K = map(int,input().split())
adj = [ [ ]for _ in range(N) ]
comb = Combination(10**5)

def nPr(n,r):
  if n < r: return 0
  return comb(n, r) * comb.fac[r]

for _ in range(N-1):
  a,b = map(int,input().split())
  a -= 1
  b -= 1
  adj[a].append(b)
  adj[b].append(a)

def dfs(v, p=-1):
  global ans
  c = 0
  for nei in adj[v]:
    if nei == p: continue
    c += 1
    dfs(nei, v)

  nk = K-1 if p==-1 else K-2
  ans *= nPr(nk, c)
  ans %= 10**9+7

ans = K
dfs(0)
print(ans)

Buggy python submission (verdict: Runtime Error):
class Combination:
  def __init__(self, n_max, mod=10**9+7):
    self.mod = mod
    self.modinv = self.make_modinv_list(n_max)
    self.fac, self.facinv = self.make_factorial_list(n_max)

  def __call__(self, n, r):
    return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod

  def make_factorial_list(self, n):
    # 階乗のリストと階乗のmod逆元のリストを返す O(n)
    # self.make_modinv_list()が先に実行されている必要がある
    fac = [1]
    facinv = [1]
    for i in range(1, n+1):
      fac.append(fac[i-1] * i % self.mod)
      facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
    return fac, facinv

  def make_modinv_list(self, n):
    # 0からnまでのmod逆元のリストを返す O(n)
    modinv = [0] * (n+1)
    modinv[1] = 1
    for i in range(2, n+1):
        modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
    return modinv

N,K = map(int,input().split())
adj = [ [ ]for _ in range(N) ]
comb = Combination(10**5)

def nPr(n,r):
  return comb(n, r) * comb.fac[r]

for _ in range(N-1):
  a,b = map(int,input().split())
  a -= 1
  b -= 1
  adj[a].append(b)
  adj[b].append(a)

def dfs(v, p=-1):
  global ans
  c = 0
  for nei in adj[v]:
    if nei == p: continue
    c += 1
    dfs(nei, v)

  nk = K-1 if p==-1 else K-2
  ans *= nPr(nk, c)
  ans %= 10**9+7

ans = K
dfs(0)
print(ans)

Fixed submission:
import sys
sys.setrecursionlimit(10**9)
class Combination:
  def __init__(self, n_max, mod=10**9+7):
    self.mod = mod
    self.modinv = self.make_modinv_list(n_max)
    self.fac, self.facinv = self.make_factorial_list(n_max)

  def __call__(self, n, r):
    return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod

  def make_factorial_list(self, n):
    # 階乗のリストと階乗のmod逆元のリストを返す O(n)
    # self.make_modinv_list()が先に実行されている必要がある
    fac = [1]
    facinv = [1]
    for i in range(1, n+1):
      fac.append(fac[i-1] * i % self.mod)
      facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
    return fac, facinv

  def make_modinv_list(self, n):
    # 0からnまでのmod逆元のリストを返す O(n)
    modinv = [0] * (n+1)
    modinv[1] = 1
    for i in range(2, n+1):
        modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
    return modinv

N,K = map(int,input().split())
adj = [ [ ]for _ in range(N) ]
comb = Combination(10**5)

def nPr(n,r):
  if n < r: return 0
  return comb(n, r) * comb.fac[r]

for _ in range(N-1):
  a,b = map(int,input().split())
  a -= 1
  b -= 1
  adj[a].append(b)
  adj[b].append(a)

def dfs(v, p=-1):
  global ans
  c = 0
  for nei in adj[v]:
    if nei == p: continue
    c += 1
    dfs(nei, v)

  nk = K-1 if p==-1 else K-2
  ans *= nPr(nk, c)
  ans %= 10**9+7

ans = K
dfs(0)
print(ans)