Buggy python submission (verdict: Runtime Error):
n, m = map(int, input().split())
temp = [0] * (n + 1)
temp[0] = 0
temp[1] = 1
temp[2] = 2
for i in range(3, n + 1):
  temp[i] = temp[i-1] + temp[i-2]

mod = 10 ** 9 + 7
start = 0
cnt = 1
for i in range(m):
  ko = int(input())
  if ko == 1:
    start = ko + 1
    continue
  end = ko - 1
  diff = end - start
  if diff < 0:
    diff = 0
  if diff == 0:
    start = ko + 1
    continue
  cnt = cnt * temp[diff]
  start = ko + 1

if n - start != 0:
  cnt = cnt * temp[n - start]
print(cnt % mod)

Fixed submission:
n, m = map(int, input().split())
MOD = 1000000007

fact=[0,1]
fact_inv=[0]*(n+1)
for i in range(2,n+1):
  fact.append(fact[-1]*i % MOD)

fact_inv[n] = pow(fact[n],MOD-2,MOD)
for i in range(n-1,-1,-1):
  fact_inv[i] = fact_inv[i+1]*(i+1)%MOD

def comb(n,r):
  return fact[n]*fact_inv[r]*fact_inv[n-r]%MOD

def sigmaComb(dis):
  ans=0
  if dis == 1 or dis == 0:
    return 1
  end=dis//2+1
  for i in range(end):
    t=comb(dis-i,i)
    #print(dis-i,i,t)
    ans+=t
  return ans

hole=[0]
ans=1
for i in range(m):
  t = int(input())
  availLeft=hole[-1]
  availRight=t-1
  dis=availRight-availLeft
  if dis <0:
    ans=0
    break

  ans=ans*sigmaComb(dis)%MOD
  #print("dis=",dis,t,ans)
  hole.append(t+1)
else:
  availLeft=hole[-1]
  availRight=n
  dis=availRight-availLeft
  #print("dis=",dis,hole[-1],ans)
  ans=ans*sigmaComb(dis)%MOD

print(ans%MOD)

Buggy python submission (verdict: Runtime Error):
n, m = map(int, input().split())
temp = [0] * (n + 1)
temp[0] = 0
temp[1] = 1
temp[2] = 2
for i in range(3, n + 1):
  temp[i] = temp[i-1] + temp[i-2]

mod = 10 ** 9 + 7
start = 0
cnt = 1
for i in range(m):
  ko = int(input())
  if ko == 1:
    start = ko + 1
    continue
  end = ko - 1
  diff = end - start
  if diff < 0:
    diff = 0
  cnt = cnt * temp[diff]
  start = ko + 1

if n - start != 0:
  cnt = cnt * temp[n - start]
print(cnt % mod)

Fixed submission:
n, m = map(int, input().split())
MOD = 1000000007

fact=[0,1]
fact_inv=[0]*(n+1)
for i in range(2,n+1):
  fact.append(fact[-1]*i % MOD)

fact_inv[n] = pow(fact[n],MOD-2,MOD)
for i in range(n-1,-1,-1):
  fact_inv[i] = fact_inv[i+1]*(i+1)%MOD

def comb(n,r):
  return fact[n]*fact_inv[r]*fact_inv[n-r]%MOD

def sigmaComb(dis):
  ans=0
  if dis == 1 or dis == 0:
    return 1
  end=dis//2+1
  for i in range(end):
    t=comb(dis-i,i)
    #print(dis-i,i,t)
    ans+=t
  return ans

hole=[0]
ans=1
for i in range(m):
  t = int(input())
  availLeft=hole[-1]
  availRight=t-1
  dis=availRight-availLeft
  if dis <0:
    ans=0
    break

  ans=ans*sigmaComb(dis)%MOD
  #print("dis=",dis,t,ans)
  hole.append(t+1)
else:
  availLeft=hole[-1]
  availRight=n
  dis=availRight-availLeft
  #print("dis=",dis,hole[-1],ans)
  ans=ans*sigmaComb(dis)%MOD

print(ans%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

mod = 10 ** 9 + 7
def combinations_count(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

def pat(n):
  cnt = 0
  for i in range(n//2 + 1):
    cnt += int(combinations_count(n - i, i))
  return cnt

n, m = map(int, input().split())
a = []
start = 0
cnt = 1
for i in range(m):
  ko = int(input())
  end = ko - 1
  cnt = cnt * pat(end - start)
  start = ko + 1
cnt = cnt * pat(n - start)

print(cnt % mod)
  

Fixed submission:
n, m = map(int, input().split())
MOD = 1000000007

fact=[0,1]
fact_inv=[0]*(n+1)
for i in range(2,n+1):
  fact.append(fact[-1]*i % MOD)

fact_inv[n] = pow(fact[n],MOD-2,MOD)
for i in range(n-1,-1,-1):
  fact_inv[i] = fact_inv[i+1]*(i+1)%MOD

def comb(n,r):
  return fact[n]*fact_inv[r]*fact_inv[n-r]%MOD

def sigmaComb(dis):
  ans=0
  if dis == 1 or dis == 0:
    return 1
  end=dis//2+1
  for i in range(end):
    t=comb(dis-i,i)
    #print(dis-i,i,t)
    ans+=t
  return ans

hole=[0]
ans=1
for i in range(m):
  t = int(input())
  availLeft=hole[-1]
  availRight=t-1
  dis=availRight-availLeft
  if dis <0:
    ans=0
    break

  ans=ans*sigmaComb(dis)%MOD
  #print("dis=",dis,t,ans)
  hole.append(t+1)
else:
  availLeft=hole[-1]
  availRight=n
  dis=availRight-availLeft
  #print("dis=",dis,hole[-1],ans)
  ans=ans*sigmaComb(dis)%MOD

print(ans%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

mod = 10 ** 9 + 7
def combinations_count(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

def pat(n):
  cnt = 0
  for i in range(n//2 + 1):
    cnt += int(combinations_count(n - i, i))
  return cnt

n, m = map(int, input().split())
a = []
start = 0
cnt = 1
for i in range(m):
  ko = int(input())
  end = ko - 1
  cnt = cnt * pat(end - start)
  start = ko + 1
cnt = cnt * pat(n - start)

print(cnt % mod)

Fixed submission:
n, m = map(int, input().split())
MOD = 1000000007

fact=[0,1]
fact_inv=[0]*(n+1)
for i in range(2,n+1):
  fact.append(fact[-1]*i % MOD)

fact_inv[n] = pow(fact[n],MOD-2,MOD)
for i in range(n-1,-1,-1):
  fact_inv[i] = fact_inv[i+1]*(i+1)%MOD

def comb(n,r):
  return fact[n]*fact_inv[r]*fact_inv[n-r]%MOD

def sigmaComb(dis):
  ans=0
  if dis == 1 or dis == 0:
    return 1
  end=dis//2+1
  for i in range(end):
    t=comb(dis-i,i)
    #print(dis-i,i,t)
    ans+=t
  return ans

hole=[0]
ans=1
for i in range(m):
  t = int(input())
  availLeft=hole[-1]
  availRight=t-1
  dis=availRight-availLeft
  if dis <0:
    ans=0
    break

  ans=ans*sigmaComb(dis)%MOD
  #print("dis=",dis,t,ans)
  hole.append(t+1)
else:
  availLeft=hole[-1]
  availRight=n
  dis=availRight-availLeft
  #print("dis=",dis,hole[-1],ans)
  ans=ans*sigmaComb(dis)%MOD

print(ans%MOD)