Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(100000000)
def mod_combination(n, k, mod):
    def mod_permutation(n, k, mod):
        if n<=k:
            return 1
        else:
            return (n * mod_permutation(n-1,k,mod))%mod

    def mod_inv_permutation(k, mod):
        k, mod = int(k), int(mod)
        if k<=1:
            return 1
        else:
            return (pow(k,mod-2,mod) * mod_inv_permutation(k-1, mod))%mod

    return (mod_permutation(n,n-k,mod) * mod_inv_permutation(k, mod))%mod

n,a,b=map(int,input().split())
mod=1000000007
print((pow(2,n,mod)-1-mod_combination(n, a, mod)-mod_combination(n, b, mod))%mod)

Fixed submission:
def power(x, a):
    if a == 0:
        return 1
    elif a == 1:
        return x
    elif a % 2 == 0:
        return power(x, a//2) **2 % mod
    else:
        return power(x, a//2) **2 * x % mod

def modinv(x):
    return power(x, mod-2)

def binomial_coefficients(n, k):
    numera = 1  
    denomi = 1  

    for i in range(k):
        numera *= n-i
        numera %= mod
        denomi *= i+1
        denomi %= mod
    return numera * modinv(denomi) % mod

n,a,b=map(int,input().split())
mod=1000000007
print((pow(2,n,mod)-1-binomial_coefficients(n, a)-binomial_coefficients(n, b))%mod)

Buggy python submission (verdict: Runtime Error):
import sys 
sys.setrecursionlimit(10**10)

def mod_combination(n, k, mod):
    def mod_permutation(n, k, mod):
        if n<=k:
            return 1
        else:
            return (n * mod_permutation(n-1,k,mod))%mod

    def mod_inv_permutation(k, mod):
        k, mod = int(k), int(mod)
        if k<=1:
            return 1
        else:
            return (pow(k,mod-2,mod) * mod_inv_permutation(k-1, mod))%mod

    return (mod_permutation(n,n-k,mod) * mod_inv_permutation(k, mod))%mod

n,a,b=map(int,input().split())
mod=1000000007
print(pow(2,n,mod)-1-mod_combination(n, a, mod)-mod_combination(n, b, mod))

Fixed submission:
def power(x, a):
    if a == 0:
        return 1
    elif a == 1:
        return x
    elif a % 2 == 0:
        return power(x, a//2) **2 % mod
    else:
        return power(x, a//2) **2 * x % mod

def modinv(x):
    return power(x, mod-2)

def binomial_coefficients(n, k):
    numera = 1  
    denomi = 1  

    for i in range(k):
        numera *= n-i
        numera %= mod
        denomi *= i+1
        denomi %= mod
    return numera * modinv(denomi) % mod

n,a,b=map(int,input().split())
mod=1000000007
print((pow(2,n,mod)-1-binomial_coefficients(n, a)-binomial_coefficients(n, b))%mod)

Buggy python submission (verdict: Runtime Error):
def mod_combination(n, k, mod):
    def mod_permutation(n, k, mod):
        if n<=k:
            return 1
        else:
            return (n * mod_permutation(n-1,k,mod))%mod

    def mod_inv_permutation(k, mod):
        k, mod = int(k), int(mod)
        if k<=1:
            return 1
        else:
            return (pow(k,mod-2,mod) * mod_inv_permutation(k-1, mod))%mod

    return (mod_permutation(n,n-k,mod) * mod_inv_permutation(k, mod))%mod

n,a,b=map(int,input().split())
mod=1000000007
print(pow(2,n,mod)-1-mod_combination(n, a, mod)-mod_combination(n, b, mod))

Fixed submission:
def power(x, a):
    if a == 0:
        return 1
    elif a == 1:
        return x
    elif a % 2 == 0:
        return power(x, a//2) **2 % mod
    else:
        return power(x, a//2) **2 * x % mod

def modinv(x):
    return power(x, mod-2)

def binomial_coefficients(n, k):
    numera = 1  
    denomi = 1  

    for i in range(k):
        numera *= n-i
        numera %= mod
        denomi *= i+1
        denomi %= mod
    return numera * modinv(denomi) % mod

n,a,b=map(int,input().split())
mod=1000000007
print((pow(2,n,mod)-1-binomial_coefficients(n, a)-binomial_coefficients(n, b))%mod)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def f(N, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

n,a,b=map(int,input().split())
mod=1000000007
x=n//100
y=n%100
s=((x*976371285)%mod+(2**y)%mod)%mod
A=f(n,a)%mod
B=f(n,b)%mod
print(s-A-B-1)

Fixed submission:
def power(x, a):
    if a == 0:
        return 1
    elif a == 1:
        return x
    elif a % 2 == 0:
        return power(x, a//2) **2 % mod
    else:
        return power(x, a//2) **2 * x % mod

def modinv(x):
    return power(x, mod-2)

def binomial_coefficients(n, k):
    numera = 1  
    denomi = 1  

    for i in range(k):
        numera *= n-i
        numera %= mod
        denomi *= i+1
        denomi %= mod
    return numera * modinv(denomi) % mod

n,a,b=map(int,input().split())
mod=1000000007
print((pow(2,n,mod)-1-binomial_coefficients(n, a)-binomial_coefficients(n, b))%mod)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def f(N, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

n,a,b=map(int,input().split())
mod=1000000007
s=(2**n)%mod
A=f(n,a)%mod
B=f(n,b)%mod
print(s-A-B-1)

Fixed submission:
def power(x, a):
    if a == 0:
        return 1
    elif a == 1:
        return x
    elif a % 2 == 0:
        return power(x, a//2) **2 % mod
    else:
        return power(x, a//2) **2 * x % mod

def modinv(x):
    return power(x, mod-2)

def binomial_coefficients(n, k):
    numera = 1  
    denomi = 1  

    for i in range(k):
        numera *= n-i
        numera %= mod
        denomi *= i+1
        denomi %= mod
    return numera * modinv(denomi) % mod

n,a,b=map(int,input().split())
mod=1000000007
print((pow(2,n,mod)-1-binomial_coefficients(n, a)-binomial_coefficients(n, b))%mod)