Buggy python submission (verdict: Time Limit Exceeded):
N, a, b = map(int,input().split())
mod = 10**9+7

def prepare(n, mod):
    f = 1
    factorials = [1]
    for m in range(1, n + 1):
        f *= m
        f %= mod
        factorials.append(f)
    inv = pow(f, mod - 2, mod)
    invs = [1] * (n + 1)
    invs[n] = inv
    for m in range(n, 1, -1):
        inv *= m
        inv %= mod
        invs[m - 1] = inv
    return factorials, invs

factorials, invs = prepare(N,mod)
sum = 1
for i in range(N) :
    sum = (sum * 2) % mod

nCa = (factorials[N] * invs[N-a] % mod * invs[a] % mod)
nCb = (factorials[N] * invs[N-b] % mod * invs[b] % mod)

sum = (sum - nCa - nCb - 1) % mod
print(sum)


Fixed submission:
n, a, b = map(int, input().split())
mod = 10**9 + 7

def comb(n, r, mod):
    X = 1
    Y = 1
    for i in range(1,r+1):
        X = (X*(n-i+1))%mod
        Y = (Y*i)%mod
    return (X*pow(Y, mod-2, mod))%mod

ans = (pow(2, n, mod) -1 - comb(n, a, mod) - comb(n, b, mod))%mod
print(ans)

Buggy python submission (verdict: Runtime Error):
class ModTools:
    def __init__(self, MAX, MOD):
        MAX += 1
        self.MAX = MAX
        self.MOD = MOD
        factorial = [1] * MAX
        factorial[0] = factorial[1] = 1
        for i in range(2, MAX):
            factorial[i] = factorial[i-1] * i % MOD
        inverse = [1] * MAX
        inverse[MAX-1] = pow(factorial[MAX-1], MOD-2, MOD)
        for i in range(MAX-2, 0, -1):
            inverse[i] = inverse[i+1] * (i+1) % MOD
        self.fact = factorial
        self.inv = inverse

    def nCr(self, n, r):
        if n < r: return 0
        r = min(r, n-r)
        numerator = self.fact[n]
        denominator = self.inv[r] * self.inv[n-r] % self.MOD
        return numerator * denominator % self.MOD

N, a, b = map(int,input().split())
mod = 10**9+7
fact = ModTools(N, mod)
sum = 1
for i in range(N) :
    sum = (sum * 2) % mod

sum = (sum - fact.nCr(N,a) - fact.nCr(N,b) - 1) % mod
print(sum)


Fixed submission:
n, a, b = map(int, input().split())
mod = 10**9 + 7

def comb(n, r, mod):
    X = 1
    Y = 1
    for i in range(1,r+1):
        X = (X*(n-i+1))%mod
        Y = (Y*i)%mod
    return (X*pow(Y, mod-2, mod))%mod

ans = (pow(2, n, mod) -1 - comb(n, a, mod) - comb(n, b, mod))%mod
print(ans)

Buggy python submission (verdict: Runtime Error):
class Factorial:
    def __init__(self, n, mod=10**9+7):
        self.fac = [0] * (n+1)
        self.ifac = [0] * (n+1)
        self.fac[0] = 1
        self.ifac[0] = 1
        self.mod = mod
        modmod = self.mod - 2
        for i in range(n):
            self.fac[i+1] = self.fac[i] * (i+1) % self.mod
            self.ifac[i+1] = self.ifac[i] * pow(i+1, modmod, self.mod) % self.mod

    def comb(self, n, r):
        if n == 0 and r == 0:
            return 1
        if n < r or n < 0:
            return 0
        tmp =  self.ifac[n-r] * self.ifac[r] % self.mod
        return tmp * self.fac[n] % self.mod

    def perm(self, n, r):
        if n == 0 and r == 0:
            return 1
        if n < r or n < 0:
            return 0
        return (self.fac[n] * self.ifac[n-r]) % self.mod


N, a, b = map(int,input().split())
mod = 10**9+7

fact = Factorial(N)
sum = 1
for i in range(N) :
    sum = (sum * 2) % mod

sum = (sum - fact.comb(N,a) - fact.comb(N,b) - 1) % mod
print(sum)

Fixed submission:
n, a, b = map(int, input().split())
mod = 10**9 + 7

def comb(n, r, mod):
    X = 1
    Y = 1
    for i in range(1,r+1):
        X = (X*(n-i+1))%mod
        Y = (Y*i)%mod
    return (X*pow(Y, mod-2, mod))%mod

ans = (pow(2, n, mod) -1 - comb(n, a, mod) - comb(n, b, mod))%mod
print(ans)

Buggy python submission (verdict: Runtime Error):
class Factorial:
    def __init__(self, n, mod=10**9+7):
        self.fac = [0] * (n+1)
        self.ifac = [0] * (n+1)
        self.fac[0] = 1
        self.ifac[0] = 1
        self.mod = mod
        modmod = self.mod - 2
        for i in range(n):
            self.fac[i+1] = self.fac[i] * (i+1) % self.mod
            self.ifac[i+1] = self.ifac[i] * pow(i+1, modmod, self.mod) % self.mod

    def comb(self, n, r):
        if n == 0 and r == 0:
            return 1
        if n < r or n < 0:
            return 0
        tmp =  self.ifac[n-r] * self.ifac[r] % self.mod
        return tmp * self.fac[n] % self.mod

    def perm(self, n, r):
        if n == 0 and r == 0:
            return 1
        if n < r or n < 0:
            return 0
        return (self.fac[n] * self.ifac[n-r]) % self.mod

N, a, b = map(int,input().split())
mod = 10**9+7

fact = Factorial(N)
sum = 0
for i in range(N) :
    sum = (sum + fact.comb(N,i)) % mod

sum = (sum - fact.comb(N,a) - fact.comb(N,b)) % mod
print(sum)

Fixed submission:
n, a, b = map(int, input().split())
mod = 10**9 + 7

def comb(n, r, mod):
    X = 1
    Y = 1
    for i in range(1,r+1):
        X = (X*(n-i+1))%mod
        Y = (Y*i)%mod
    return (X*pow(Y, mod-2, mod))%mod

ans = (pow(2, n, mod) -1 - comb(n, a, mod) - comb(n, b, mod))%mod
print(ans)