Buggy python submission (verdict: Runtime Error):
MAX_N = 10**5+1
DP = [None] * (MAX_N + 1)  # 計算結果を保存する配列
DP[0] = 0  # 定義より
DP[1] = 1  # 定義より

def fib(n):
    # フィボナッチ数を2からnまで順に求めていく
    for i in range(2, n + 1):
        DP[i] = DP[i-1] + DP[i-2]
    return DP[n]

MOD = 10**9 + 7

N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]

ans = fib(a[0])
for i in range(M-1):
    ans *= fib(a[i+1] - a[i] - 1)
    ans %= MOD
ans *= fib(N - a[M-1])
ans %= MOD

print(ans)


Fixed submission:
from itertools import product

INF = 1000000007

def mat2_mul(X, Y):
	z = [[0, 0], [0, 0]]
	for (i, j, k) in product(range(2), range(2), range(2)):
		z[i][j] += X[i][k] * Y[k][j]
	return z

def mat2_pow(X, n):
	if n == 0:
		return [[1, 0], [0, 1]]
	elif n % 2:
		return mat2_mul(X, mat2_pow(X, n - 1))
	else:
		half_pow = mat2_pow(X, n / 2)
		return mat2_mul(half_pow, half_pow)

def fib(n):
	if n == 0:
		return 0
	else:
		f = [[0, 1], [1, 1]]
	return mat2_pow(f, n - 1)[1][1]


N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
ans, start = 1, 0
tmp = []

for i in range(len(a)):
	if a[i] - a[i - 1] == 1:
		print(0)
		exit()

for k in a:
	tmp.append(fib(k - start) % INF)
	start = k + 1

for j in tmp:
	ans *= j
	ans %= INF

ans *= fib(N - start + 1)
print(ans % INF)

Buggy python submission (verdict: Runtime Error):
MAX_N = 10**5
DP = [None] * (MAX_N + 1)  # 計算結果を保存する配列
DP[0] = 0  # 定義より
DP[1] = 1  # 定義より

def fib(n):
    # フィボナッチ数を2からnまで順に求めていく
    for i in range(2, n + 1):
        DP[i] = DP[i-1] + DP[i-2]
    return DP[n]

MOD = 10**9 + 7

N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]

ans = fib(a[0])
for i in range(M-1):
    ans *= fib(a[i+1] - a[i] - 1)
    ans %= MOD
ans *= fib(N - a[M-1])
ans %= MOD

print(ans)


Fixed submission:
from itertools import product

INF = 1000000007

def mat2_mul(X, Y):
	z = [[0, 0], [0, 0]]
	for (i, j, k) in product(range(2), range(2), range(2)):
		z[i][j] += X[i][k] * Y[k][j]
	return z

def mat2_pow(X, n):
	if n == 0:
		return [[1, 0], [0, 1]]
	elif n % 2:
		return mat2_mul(X, mat2_pow(X, n - 1))
	else:
		half_pow = mat2_pow(X, n / 2)
		return mat2_mul(half_pow, half_pow)

def fib(n):
	if n == 0:
		return 0
	else:
		f = [[0, 1], [1, 1]]
	return mat2_pow(f, n - 1)[1][1]


N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
ans, start = 1, 0
tmp = []

for i in range(len(a)):
	if a[i] - a[i - 1] == 1:
		print(0)
		exit()

for k in a:
	tmp.append(fib(k - start) % INF)
	start = k + 1

for j in tmp:
	ans *= j
	ans %= INF

ans *= fib(N - start + 1)
print(ans % INF)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
INF = 1000000007

dp = [0] * (N + 1)
dp[0] = 1
if 1 not in a:
	dp[1] = 1
else:
	dp[1] = 0
for i in range(2, N + 1):
	if i in a:
		continue
	dp[i] = dp[i - 1] + dp[i - 2]
	dp[i] %= INF

print(dp[N])


Fixed submission:
from itertools import product

INF = 1000000007

def mat2_mul(X, Y):
	z = [[0, 0], [0, 0]]
	for (i, j, k) in product(range(2), range(2), range(2)):
		z[i][j] += X[i][k] * Y[k][j]
	return z

def mat2_pow(X, n):
	if n == 0:
		return [[1, 0], [0, 1]]
	elif n % 2:
		return mat2_mul(X, mat2_pow(X, n - 1))
	else:
		half_pow = mat2_pow(X, n / 2)
		return mat2_mul(half_pow, half_pow)

def fib(n):
	if n == 0:
		return 0
	else:
		f = [[0, 1], [1, 1]]
	return mat2_pow(f, n - 1)[1][1]


N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
ans, start = 1, 0
tmp = []

for i in range(len(a)):
	if a[i] - a[i - 1] == 1:
		print(0)
		exit()

for k in a:
	tmp.append(fib(k - start) % INF)
	start = k + 1

for j in tmp:
	ans *= j
	ans %= INF

ans *= fib(N - start + 1)
print(ans % INF)

Buggy python submission (verdict: Time Limit Exceeded):
from itertools import product

INF = 1000000007

def mat2_mul(X, Y):
	Z = [[0, 0], [0, 0]]
	for (i, j, k) in product(range(2), range(2), range(2)):
		Z[i][j] += X[i][k] * Y[k][j]
	return Z

def mat2_pow(X, n):
	if n == 0:
		return [[1, 0], [0, 1]]
	elif n % 2:
		return mat2_mul(X, mat2_pow(X, n - 1))
	else:
		half_pow = mat2_pow(X, n / 2)
		return mat2_mul(half_pow, half_pow)

def fib(n):
	if n == 0:
		return 0
	else:
		F = [[0, 1], [1, 1]]
	return mat2_pow(F, n - 1)[1][1] % INF


N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
a = list(set(a))
ans, start = 1, 0

for j in range(1, M):
	if a[j] - a[j - 1] == 1:
		print(0)
		exit()

for k in range(N):
	if k in a:
		ans *= fib(k - start)
		ans %= INF
		start = k + 1
ans *= fib(N - start + 1)
print(ans % INF)


Fixed submission:
from itertools import product

INF = 1000000007

def mat2_mul(X, Y):
	z = [[0, 0], [0, 0]]
	for (i, j, k) in product(range(2), range(2), range(2)):
		z[i][j] += X[i][k] * Y[k][j]
	return z

def mat2_pow(X, n):
	if n == 0:
		return [[1, 0], [0, 1]]
	elif n % 2:
		return mat2_mul(X, mat2_pow(X, n - 1))
	else:
		half_pow = mat2_pow(X, n / 2)
		return mat2_mul(half_pow, half_pow)

def fib(n):
	if n == 0:
		return 0
	else:
		f = [[0, 1], [1, 1]]
	return mat2_pow(f, n - 1)[1][1]


N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
ans, start = 1, 0
tmp = []

for i in range(len(a)):
	if a[i] - a[i - 1] == 1:
		print(0)
		exit()

for k in a:
	tmp.append(fib(k - start) % INF)
	start = k + 1

for j in tmp:
	ans *= j
	ans %= INF

ans *= fib(N - start + 1)
print(ans % INF)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
INF = 1000000007
a = list(set(a))

ans, start = 1, 0

x = [1] * (N + 1)  #x[i]は0からiまでの階段の移動方法の数
x[0], x[1] = 1, 1
for i in range(2, N + 1):
	x[i] = (x[i - 1] + x[i - 2]) % INF

for j in range(1, M):
	if a[j] - a[j - 1] == 1:
		print(0)
		exit()

for k in range(N):
	if k in a:
		# print("hit")
		ans *= x[k - 1 - start]
		ans %= INF
		start = k + 1
	# print(k, "now", ans)
ans *= x[N - start]
print(ans % INF)


Fixed submission:
from itertools import product

INF = 1000000007

def mat2_mul(X, Y):
	z = [[0, 0], [0, 0]]
	for (i, j, k) in product(range(2), range(2), range(2)):
		z[i][j] += X[i][k] * Y[k][j]
	return z

def mat2_pow(X, n):
	if n == 0:
		return [[1, 0], [0, 1]]
	elif n % 2:
		return mat2_mul(X, mat2_pow(X, n - 1))
	else:
		half_pow = mat2_pow(X, n / 2)
		return mat2_mul(half_pow, half_pow)

def fib(n):
	if n == 0:
		return 0
	else:
		f = [[0, 1], [1, 1]]
	return mat2_pow(f, n - 1)[1][1]


N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
ans, start = 1, 0
tmp = []

for i in range(len(a)):
	if a[i] - a[i - 1] == 1:
		print(0)
		exit()

for k in a:
	tmp.append(fib(k - start) % INF)
	start = k + 1

for j in tmp:
	ans *= j
	ans %= INF

ans *= fib(N - start + 1)
print(ans % INF)