Buggy python submission (verdict: Time Limit Exceeded):
from sys import setrecursionlimit
setrecursionlimit(10 ** 8)

n, k = [int(i) for i in input().split()]
A = [[int(i) for i in input().split()] for j in range(n - 1)]
p = 10 ** 9 + 7

E = [[] for i in range(n + 1)]

for a, b in A:
    E[a].append(b)
    E[b].append(a)

visited = [False] * (n + 1)

def dfs(i, f, s):
    if visited[i]:
        return 1
    b = f + s
    visited[i] = True
    
    res = k - b
    s = f
    f = 1
    for v in E[i]:
        if visited[v]:
            continue
        res *= dfs(v, f, s)
        res %= p
        s += 1

    return res if res > 0 else 0

print(dfs(1, 0, 0))

Fixed submission:
from sys import setrecursionlimit
setrecursionlimit(10 ** 8)

n, k = [int(i) for i in input().split()]
A = [[int(i) for i in input().split()] for j in range(n - 1)]
p = 10 ** 9 + 7

E = [[] for i in range(n + 1)]

for a, b in A:
    E[a].append(b)
    E[b].append(a)

visited = [False] * (n + 1)

def dfs(i, f, s):
    if visited[i]:
        return 1
    b = f + s
    visited[i] = True
    
    res = k - b
    s = f
    f = 1
    for v in E[i]:
        if visited[v]:
            continue
        res *= dfs(v, f, s)
        res %= p
        s += 1

    return res if res > 0 else 0

print(dfs(1, 0, 0) % p)

Buggy python submission (verdict: Runtime Error):
n, k = [int(i) for i in input().split()]
A = [[int(i) for i in input().split()] for j in range(n - 1)]
p = 10 ** 9 + 7

E = [[] for i in range(n + 1)]

for a, b in A:
    E[a].append(b)
    E[b].append(a)

visited = [False] * (n + 1)

def dfs(i, f, s):
    if visited[i]:
        return 1
    b = f + s
    visited[i] = True
    
    res = k - b
    s = f
    f = 1
    for v in E[i]:
        if visited[v]:
            continue
        res *= dfs(v, f, s)
        res %= p
        s += 1

    return res if res > 0 else 0

print(dfs(1, 0, 0))

Fixed submission:
from sys import setrecursionlimit
setrecursionlimit(10 ** 8)

n, k = [int(i) for i in input().split()]
A = [[int(i) for i in input().split()] for j in range(n - 1)]
p = 10 ** 9 + 7

E = [[] for i in range(n + 1)]

for a, b in A:
    E[a].append(b)
    E[b].append(a)

visited = [False] * (n + 1)

def dfs(i, f, s):
    if visited[i]:
        return 1
    b = f + s
    visited[i] = True
    
    res = k - b
    s = f
    f = 1
    for v in E[i]:
        if visited[v]:
            continue
        res *= dfs(v, f, s)
        res %= p
        s += 1

    return res if res > 0 else 0

print(dfs(1, 0, 0) % p)

Buggy python submission (verdict: Runtime Error):
n, k = [int(i) for i in input().split()]
A = [[int(i) for i in input().split()] for j in range(n - 1)]
p = 10 ** 9 + 7

E = [[] for i in range(n + 1)]

for a, b in A:
    E[a].append(b)
    E[b].append(a)

visited = [False] * (n + 1)

def dfs2(i, k):
    if k > 2:
        return 0
    res = 0
    for v in E[i]:
        res += dfs2(v, k + 1)
    return res + visited[i]

def dfs(i):
    if visited[i]:
        return 1
    b = dfs2(i, 0)
    visited[i] = True
    
    res = k - b
    for v in E[i]:
        res *= dfs(v)
        res %= p

    return res if res > 0 else 0

print(dfs(1))

Fixed submission:
from sys import setrecursionlimit
setrecursionlimit(10 ** 8)

n, k = [int(i) for i in input().split()]
A = [[int(i) for i in input().split()] for j in range(n - 1)]
p = 10 ** 9 + 7

E = [[] for i in range(n + 1)]

for a, b in A:
    E[a].append(b)
    E[b].append(a)

visited = [False] * (n + 1)

def dfs(i, f, s):
    if visited[i]:
        return 1
    b = f + s
    visited[i] = True
    
    res = k - b
    s = f
    f = 1
    for v in E[i]:
        if visited[v]:
            continue
        res *= dfs(v, f, s)
        res %= p
        s += 1

    return res if res > 0 else 0

print(dfs(1, 0, 0) % p)