Buggy python submission (verdict: Runtime Error):
import math
import sys
sys.setrecursionlimit(100000)
f = math.factorial
n, m = map(int, input().split())
a = [-1] + [int(input()) for i in range(m)] + [n+1]
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10 ** 9 + 7
N = 10 ** 4  # N は必要分だけ用意する
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]
 
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)


count = 1
for i in range(m+1):
    k = a[i+1] - a[i] - 2
    if k == -1:
        count = 0
        break
    else:
        work = 0
        for b in range(k//2+1):
            work += cmb(k-b, b, p)
        count *= work
print(count%p)


Fixed submission:
import math
import sys
sys.setrecursionlimit(100000)
f = math.factorial
n, m = map(int, input().split())
a = [-1] + [int(input()) for i in range(m)] + [n+1]
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10 ** 9 + 7
N = 10 ** 5  # N は必要分だけ用意する
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]
 
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)


count = 1
for i in range(m+1):
    k = a[i+1] - a[i] - 2
    if k == -1:
        count = 0
        break
    else:
        work = 0
        for b in range(k//2+1):
            work += cmb(k-b, b, p)
        count *= work
print(count%p)

Buggy python submission (verdict: Time Limit Exceeded):
import math
n, m = map(int, input().split())
a = [-1] + [int(input()) for i in range(m)] + [n+1]
func = math.factorial
count = 1
for i in range(m+1):
    k = a[i+1] - a[i] - 2
    if k == -1:
        count = 0
        break
    else:
        work = 0
        for b in range(k//2+1):
            work += func(k-b)//(func(k-2*b)*func(b))
        count *= work
print(count%1000000007)

Fixed submission:
import math
import sys
sys.setrecursionlimit(100000)
f = math.factorial
n, m = map(int, input().split())
a = [-1] + [int(input()) for i in range(m)] + [n+1]
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10 ** 9 + 7
N = 10 ** 5  # N は必要分だけ用意する
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]
 
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)


count = 1
for i in range(m+1):
    k = a[i+1] - a[i] - 2
    if k == -1:
        count = 0
        break
    else:
        work = 0
        for b in range(k//2+1):
            work += cmb(k-b, b, p)
        count *= work
print(count%p)

Buggy python submission (verdict: Time Limit Exceeded):
import math
n, m = map(int, input().split())
a = [-1] + [int(input()) for i in range(m)] + [n+1]
func = math.factorial
count = 1
for i in range(m+1):
    k = a[i+1] - a[i] - 2
    if k == -1:
        count = 0
        break
    else:
        work = 0
        for b in range(k//2+1):
            work += func(k-b)//(func(k-2*b)*func(b))
        count *= work
print(count%1000000007)

Fixed submission:
import math
import sys
sys.setrecursionlimit(100000)
f = math.factorial
n, m = map(int, input().split())
a = [-1] + [int(input()) for i in range(m)] + [n+1]
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10 ** 9 + 7
N = 10 ** 5  # N は必要分だけ用意する
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]
 
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)


count = 1
for i in range(m+1):
    k = a[i+1] - a[i] - 2
    if k == -1:
        count = 0
        break
    else:
        work = 0
        for b in range(k//2+1):
            work += cmb(k-b, b, p)
        count *= work
print(count%p)

Buggy python submission (verdict: Time Limit Exceeded):
import math
n, m = map(int, input().split())
a = [-1] + [int(input()) for i in range(m)] + [n+1]
a.append(n+1)
func = math.factorial
count = 1
for i in range(m+1):
    k = a[i+1] - a[i] - 2
    if k == -1:
        count = 0
        break
    else:
        work = 0
        for b in range(k//2+1):
            work += func(k-b)//(func(k-2*b)*func(b))
        count *= work
print(count%1000000007)

Fixed submission:
import math
import sys
sys.setrecursionlimit(100000)
f = math.factorial
n, m = map(int, input().split())
a = [-1] + [int(input()) for i in range(m)] + [n+1]
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10 ** 9 + 7
N = 10 ** 5  # N は必要分だけ用意する
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]
 
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)


count = 1
for i in range(m+1):
    k = a[i+1] - a[i] - 2
    if k == -1:
        count = 0
        break
    else:
        work = 0
        for b in range(k//2+1):
            work += cmb(k-b, b, p)
        count *= work
print(count%p)