Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        num -= 1
        queue.append(node)
    answer %= MOD

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                num -= 1
                queue.append(child_node)

        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def permutations_count(n, r):
    if r>n or r<0:
        return 0
    ret = 1
    for i in range(n - r + 1, n + 1):
        ret *= i
        ret %= MOD
    return ret

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    answer *= permutations_count(K-1,len(matrix[1]))
    for node in matrix[1]:
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] == 0:
            answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
        else:
            continue
        visited[q] = 1

        for child_node in matrix[q]:
            if child_node != q:
                queue.append(child_node)

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
MOD = 1000000007  # type: int

def permutations_count(n, k):
    if k>n or k<0:
        return 0
    if k == 0:
        return 1
    return n * permutations_count(n-1, k-1) % MOD

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    answer *= permutations_count(K-1,len(matrix[1]))
    for node in matrix[1]:
        queue.append(node)

    while queue:
        q = queue.popleft()

        if visited[q] == 0:
            answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
        else:
            continue

        visited[q] = 1

        for child_node in matrix[q]:
            if child_node != q:
                queue.append(child_node)

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
MOD = 1000000007  # type: int

def permutations_count(n, k):
    if k == 0:
        return 1
    return n * permutations_count(n-1, k-1) % MOD

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K

    if K-1 < len(matrix[1]):
        print(0)
        return

    answer *= permutations_count(K-1,len(matrix[1]))
    for node in matrix[1]:
        queue.append(node)

    while queue:
        q = queue.popleft()

        if visited[q] == 0:
            if K-2 < len(matrix[q])-1:
                print(0)
                return
            answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
        else:
            continue

        visited[q] = 1

        for child_node in matrix[q]:
            if child_node != q:
                queue.append(child_node)

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
MOD = 1000000007  # type: int

def permutations_count(n, k):
    if k == 0:
        return 1
    return n * permutations_count(n-1, k-1) % MOD

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K

    if K-2 < len(matrix[1])-1:
        print(0)
        return
        
    answer *= permutations_count(K-1,len(matrix[1]))
    for node in matrix[1]:
        queue.append(node)

    while queue:
        q = queue.popleft()

        if visited[q] == 0:
            if K-2 < len(matrix[q])-1:
                print(0)
                return
            answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
        else:
            continue

        visited[q] = 1

        for child_node in matrix[q]:
            if child_node != q:
                queue.append(child_node)

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
MOD = 1000000007  # type: int

def permutations_count(n, k):
    if k == 0:
        return 1
    return n * permutations_count(n-1, k-1) % MOD

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    answer *= permutations_count(K-1,len(matrix[1]))
    for node in matrix[1]:
        queue.append(node)

    while queue:
        q = queue.popleft()

        if visited[q] == 0:
            if K-2 < len(matrix[q])-1:
                print(0)
                return
            answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
        else:
            continue

        visited[q] = 1

        for child_node in matrix[q]:
            if child_node != q:
                queue.append(child_node)

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
MOD = 1000000007  # type: int

def permutations_count(n, k):
    if k == 0:
        return 1
    return n * permutations_count(n-1, k-1) % MOD

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    answer *= permutations_count(K-1,len(matrix[1]))
    for node in matrix[1]:
        queue.append(node)

    while queue:
        q = queue.popleft()

        if visited[q] == 0:
            answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
            if K-2 < len(matrix[q])-1:
                print(0)
                return
        else:
            continue

        visited[q] = 1

        for child_node in matrix[q]:
            if child_node != q:
                queue.append(child_node)

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
MOD = 1000000007  # type: int

def permutations_count(n, k):
    if k == 0:
        return 1
    return n * permutations_count(n-1, k-1) % MOD

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    answer *= permutations_count(K-1,len(matrix[1]))
    for node in matrix[1]:
        queue.append(node)

    while queue:
        q = queue.popleft()

        if visited[q] == 0:
            answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
            if K-2 < len(matrix[q])-1:
                print(0)
                return
        else:
            continue

        visited[q] = 1

        for child_node in matrix[q]:
            queue.append(child_node)

    print(answer%MOD)

    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
MOD = 1000000007  # type: int

def permutations_count(n, k):
    if k == 0:
        return 1
    return n * permutations_count(n-1, k-1) % MOD

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    answer *= permutations_count(K-1,len(matrix[1]))
    for node in matrix[1]:
        queue.append(node)

    while queue:
        q = queue.popleft()

        if visited[q] == 0:
            answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
            answer%=MOD
        else:
            continue

        visited[q] = 1

        for child_node in matrix[q]:
            queue.append(child_node)

    print(answer%MOD)

    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
MOD = 1000000007  # type: int

def permutations_count(n, k):
    if k == 0:
        return 1
    return n * permutations_count(n-1, k-1) % MOD

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque([1])
    
    answer = K
    while queue:
        q = queue.pop()
        if q == 1 and visited[q] == 0:
            answer *= permutations_count(K-1,len(matrix[1]))
        else: #q!=1 or visited==1
            if visited[q] == 0:
                answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
                answer%=MOD
            else:
                continue

        visited[q] = 1

        for child_node in matrix[q]:
            queue.append(child_node)

    print(answer%MOD)

    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
import math
MOD = 1000000007  # type: int

def permutations_count(n, r):
    return math.factorial(n) // math.factorial(n - r)

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque([1])
    
    answer = K
    while queue:
        q = queue.pop()
        if q == 1 and visited[q] == 0:
            answer *= permutations_count(K-1,len(matrix[1]))
        else: #q!=1 or visited==1
            if visited[q] == 0:
                answer *= permutations_count(K-2,len(matrix[q])-1) #親ノード引いてる
                answer%=MOD
            else:
                continue

        visited[q] = 1

        for child_node in matrix[q]:
            queue.append(child_node)

    print(answer%MOD)

    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
MOD = 1000000007  

def solve(N: int, K: int, a: "List[int]", b: "List[int]"):
    matrix = [[] for _ in range(N+1)]
    for i in range(N-1):
        matrix[a[i]].append(b[i])
        matrix[b[i]].append(a[i])
    
    visited = [0]*(N+1)

    from collections import deque
    queue = deque()
    visited[1]=1
    answer = K
    num = K-1
    for node in matrix[1]:
        answer *= num
        answer %= MOD

        num -= 1
        queue.append(node)

    while queue:
        q = queue.popleft()
        if visited[q] != 0:
            continue
        visited[q] = 1

        num = K-2
        for child_node in matrix[q]:
            if visited[child_node] == 0:
                answer *= num
                answer %= MOD
                num -= 1
                queue.append(child_node)
        answer %= MOD

    print(answer%MOD)
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    K = int(next(tokens))  # type: int
    a = [int()] * (N - 1)  # type: "List[int]"
    b = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        a[i] = int(next(tokens))
        b[i] = int(next(tokens))
    solve(N, K, a, b)

if __name__ == '__main__':
    main()