Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
if n==1 and k==1:
    print(1)
    exit()
if k==1:
    print(0)
    exit()
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
pk2=[0]*(k-1)
pk2[0]=1
for i in range(k-2):
    pk2[i+1]=pk2[i]*(k-2-i)%mod
def p(n,r):
    if n<r:
        return 0
    return pk2[r]
ans=k
q=[0]
v=[0]*n
v[0]=1
vc=1
while q and vc<n:
    s=q.pop(0)
    c=0
    if s==0:
        kai=k-1
    else:
        kai=k-2
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            vc+=1
            c+=1
            q.append(es)
            ans*=kai
            ans%=mod
            kai-=1
print(ans%mod)


Fixed submission:
from collections import deque
n,k=map(int,input().split())
if n==1 and k==1:
    print(1)
    exit()
if k==1:
    print(0)
    exit()
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
ans=k
q=deque([0])
v=[0]*n
v[0]=1
vc=1
while q and vc<n:
    s=q.popleft()
    c=0
    if s==0:
        kai=k-1
    else:
        kai=k-2
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            vc+=1
            c+=1
            q.append(es)
            ans*=kai
            ans%=mod
            kai-=1
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
if n==1 and k==1:
    print(1)
    exit()
if k==1:
    print(0)
    exit()
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
pk2=[0]*(k-1)
pk2[0]=1
for i in range(k-2):
    pk2[i+1]=pk2[i]*(k-2-i)%mod
def p(n,r):
    if n<r:
        return 0
    return pk2[r]
ans=k
q=[0]
v=[0]*n
v[0]=1
vc=1
while q and vc<n:
    s=q.pop(0)
    c=0
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            vc+=1
            c+=1
            q.append(es)
    if s==0:
        if k-1<c:
            ans=0
            break
        for i in range(k-c,k):
            ans*=i
            ans%=mod
        ans%=mod
    else:
        ans*=p(k-2,c)
        ans%=mod
print(ans%mod)


Fixed submission:
from collections import deque
n,k=map(int,input().split())
if n==1 and k==1:
    print(1)
    exit()
if k==1:
    print(0)
    exit()
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
ans=k
q=deque([0])
v=[0]*n
v[0]=1
vc=1
while q and vc<n:
    s=q.popleft()
    c=0
    if s==0:
        kai=k-1
    else:
        kai=k-2
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            vc+=1
            c+=1
            q.append(es)
            ans*=kai
            ans%=mod
            kai-=1
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
if n==1 and k==1:
    print(1)
    exit()
if k==1:
    print(0)
    exit()
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
pk2=[0]*(k-1)
pk2[0]=1
for i in range(k-2):
    pk2[i+1]=pk2[i]*(k-2-i)%mod
def p(n,r):
    if n<r:
        return 0
    return pk2[r]
ans=k
q=[0]
v=[0]*n
v[0]=1
while len(q)>0:
    s=q.pop(0)
    c=0
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            c+=1
            q.append(es)
    if s==0:
        if k-1<c:
            ans=0
            break
        for i in range(k-c,k):
            ans*=i
            ans%=mod
        ans%=mod
    else:
        ans*=p(k-2,c)
        ans%=mod
print(ans%mod)


Fixed submission:
from collections import deque
n,k=map(int,input().split())
if n==1 and k==1:
    print(1)
    exit()
if k==1:
    print(0)
    exit()
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
ans=k
q=deque([0])
v=[0]*n
v[0]=1
vc=1
while q and vc<n:
    s=q.popleft()
    c=0
    if s==0:
        kai=k-1
    else:
        kai=k-2
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            vc+=1
            c+=1
            q.append(es)
            ans*=kai
            ans%=mod
            kai-=1
print(ans%mod)

Buggy python submission (verdict: Runtime Error):
n,k=map(int,input().split())
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
pk2=[0]*(k-1)
pk2[0]=1
for i in range(k-2):
    pk2[i+1]=pk2[i]*(k-2-i)%mod
def p(n,r):
    if n<r:
        return 0
    return pk2[r]
ans=k
q=[0]
v=[0]*n
v[0]=1
while len(q)>0:
    s=q.pop(0)
    c=0
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            c+=1
            q.append(es)
    if s==0:
        for i in range(k-c,k):
            ans*=i
            ans%=mod
        ans%=mod
    else:
        ans*=p(k-2,c)
        ans%=mod
print(ans%mod)

Fixed submission:
from collections import deque
n,k=map(int,input().split())
if n==1 and k==1:
    print(1)
    exit()
if k==1:
    print(0)
    exit()
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
ans=k
q=deque([0])
v=[0]*n
v[0]=1
vc=1
while q and vc<n:
    s=q.popleft()
    c=0
    if s==0:
        kai=k-1
    else:
        kai=k-2
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            vc+=1
            c+=1
            q.append(es)
            ans*=kai
            ans%=mod
            kai-=1
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7

def p(n,r):
    if n<r:
        return 0
    re=1
    for i in range(n-r+1,n+1):
        re*=i
        re%=mod
    return re
ans=k
q=[0]
v=[0]*n
v[0]=1
while len(q)>0:
    s=q.pop(0)
    c=0
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            c+=1
            q.append(es)
    if s==0:
        ans*=p(k-1,c)
        ans%=mod
    else:
        ans*=p(k-2,c)
        ans%=mod
print(ans%mod)


Fixed submission:
from collections import deque
n,k=map(int,input().split())
if n==1 and k==1:
    print(1)
    exit()
if k==1:
    print(0)
    exit()
g=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)
mod=10**9+7
ans=k
q=deque([0])
v=[0]*n
v[0]=1
vc=1
while q and vc<n:
    s=q.popleft()
    c=0
    if s==0:
        kai=k-1
    else:
        kai=k-2
    for es in g[s]:
        if v[es]==0:
            v[es]=1
            vc+=1
            c+=1
            q.append(es)
            ans*=kai
            ans%=mod
            kai-=1
print(ans%mod)