Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
c=[[]for i in range(n+1)]
d=[False]*(n+1)
d[0]=True
m=10**9+7
for i in range(n-1):
    a,b=map(int,input().split())
    c[a].append(b)
    c[b].append(a)
p=k
t=0
pq=[1]
gd=[1,1]
sd=1
for i in range(1,k):
    sd=sd*(i+1)%m
    gd.append(sd)
while d!=[True]*(n+1):
    rom=[]
    if t==0 or t==1:
        t+=1
    for i in pq:
        d[i]=True
        q=0
        for j in c[i]:
            if d[j]==False:
                rom.append(j)
                q+=1
        else:
            if q!=0:
                if k-t>=q:
                    p=(p*(gd[k-t]*pow(gd[k-t-q],m-2,m)))%m
                else:
                    p*=0
    else:
        pq=rom[:]
print(p)

Fixed submission:
n,k=map(int,input().split())
s=[[]for i in range(n+1)]
for i in range(n-1):
    a,b=map(int,input().split())
    s[a].append(b)
    s[b].append(a)
d=[False]*(n+1)
q=[[0,1]]
c=0
a=k
while q:
    t=[]
    c=0
    for i,j in q:
        c=0
        for p in s[j]:
            if p!=i:
                t.append([j,p])
                c+=1
        r=(k-1 if j==1 else k-2)
        for h in range(r,r-c,-1):
            a=(a*h)%(10**9+7)
    q=t
print(a)

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
c=[[]for i in range(n+1)]
d=[False]*(n+1)
d[0]=True
m=10**9+7
for i in range(n-1):
    a,b=map(int,input().split())
    c[a].append(b)
    c[b].append(a)
p=k
t=0
pq=[1]
gd=[1,1]
sd=1
for i in range(1,k):
    sd=sd*(i+1)%m
    gd.append(sd)
while d!=[True]*(n+1):
    rom=[]
    if t==0 or t==1:
        t+=1
    for i in pq:
        d[i]=True
        q=0
        for j in c[i]:
            if d[j]==False:
                rom.append(j)
                q+=1
        else:
            if q!=0:
                if k-t>=q:
                    p=(p*(gd[k-t]*pow(gd[k-t-q],m-2,m)))%m
                else:
                    p*=0
    else:
        pq=rom[:]
print(p)

Fixed submission:
n,k=map(int,input().split())
s=[[]for i in range(n+1)]
for i in range(n-1):
    a,b=map(int,input().split())
    s[a].append(b)
    s[b].append(a)
d=[False]*(n+1)
q=[[0,1]]
c=0
a=k
while q:
    t=[]
    c=0
    for i,j in q:
        c=0
        for p in s[j]:
            if p!=i:
                t.append([j,p])
                c+=1
        r=(k-1 if j==1 else k-2)
        for h in range(r,r-c,-1):
            a=(a*h)%(10**9+7)
    q=t
print(a)

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
c=[[]for i in range(n+1)]
d=[False]*(n+1)
d[0]=True
m=10**9+7
for i in range(n-1):
    a,b=map(int,input().split())
    c[a].append(b)
    c[b].append(a)
p=k
t=0
pq=[1]
def fom(a,b):
    r=1
    for i in range(b):
        r=r*(a-i)%m
    return r
while d!=[True]*(n+1):
    rom=[]
    if t==0 or t==1:
        t+=1
    for i in pq:
        d[i]=True
        q=0
        for j in c[i]:
            if d[j]==False:
                rom.append(j)
                q+=1
        else:
            if k-t>=q:
                p=(p*fom(k-t,q))%m
            else:
                p*=0
    else:
        pq=rom[:]
print(p)

Fixed submission:
n,k=map(int,input().split())
s=[[]for i in range(n+1)]
for i in range(n-1):
    a,b=map(int,input().split())
    s[a].append(b)
    s[b].append(a)
d=[False]*(n+1)
q=[[0,1]]
c=0
a=k
while q:
    t=[]
    c=0
    for i,j in q:
        c=0
        for p in s[j]:
            if p!=i:
                t.append([j,p])
                c+=1
        r=(k-1 if j==1 else k-2)
        for h in range(r,r-c,-1):
            a=(a*h)%(10**9+7)
    q=t
print(a)

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
c=[[]for i in range(n+1)]
d=[False]*(n+1)
d[0]=True
m=10**9+7
for i in range(n-1):
    a,b=map(int,input().split())
    c[a].append(b)
    c[b].append(a)
p=k
t=0
pq=[1]
def fom(a,b):
    r=1
    for i in range(b):
        r=r*(a-i)%m
    return r
while d!=[True]*(n+1):
    rom=[]
    if t==0 or t==1:
        t+=1
    for i in pq:
        d[i]=True
        q=0
        for j in c[i]:
            if d[j]==False:
                rom.append(j)
                q+=1
        else:
            if k-t>=q:
                p=(p*fom(k-t,q))%m
            else:
                p*=0
    else:
        pq=rom[:]
print(p)

Fixed submission:
n,k=map(int,input().split())
s=[[]for i in range(n+1)]
for i in range(n-1):
    a,b=map(int,input().split())
    s[a].append(b)
    s[b].append(a)
d=[False]*(n+1)
q=[[0,1]]
c=0
a=k
while q:
    t=[]
    c=0
    for i,j in q:
        c=0
        for p in s[j]:
            if p!=i:
                t.append([j,p])
                c+=1
        r=(k-1 if j==1 else k-2)
        for h in range(r,r-c,-1):
            a=(a*h)%(10**9+7)
    q=t
print(a)