Buggy python submission (verdict: Runtime Error):
from functools import reduce

def inv(n):
    return p - inv(p%n) * (p//n)%p

def cmb(n, r, p):
    r = min(n - r, r)
    if r == 0:
        return 1
    numer = reduce(lambda x, y: (x*y)%p, range(n, n - r, -1))
    inv_denom = reduce(lambda x, y: (x*inv(y))%p, range(1, r + 1))
    return (numer * inv_denom) % p

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

ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)


Fixed submission:
def cmb(n, r, p):
    r = min(r, n - r)
    res = 1
    for i in range(r):
        res *= pow(i+1, p-2, p)
        res *= n-i
        res %= p
    return res

p = 10 ** 9 + 7
n, a, b = map(int, input().split())
ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)

Buggy python submission (verdict: Runtime Error):
from functools import reduce

def inv(n):
    return p - inv(p%n) * (p//n)%p

def cmb(n, r, p):
    r = min(n - r, r)
    if r == 0:
        return 1
    numer = reduce(lambda x, y: (x*y)%p, range(n, n - r, -1))
    inv_denom = reduce(lambda x, y: inv((x*y)%p), range(1, r + 1))
    return (numer * inv_denom) % p

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

ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)


Fixed submission:
def cmb(n, r, p):
    r = min(r, n - r)
    res = 1
    for i in range(r):
        res *= pow(i+1, p-2, p)
        res *= n-i
        res %= p
    return res

p = 10 ** 9 + 7
n, a, b = map(int, input().split())
ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)

Buggy python submission (verdict: Runtime Error):
from functools import reduce

def cmb(n, r, p):
    r = min(n - r, r)
    numer = reduce(lambda x, y: (x*y)%p, range(n, n - r, -1))
    denom = reduce(lambda x, y: (x*y)%p, range(1, r + 1))
    return (numer * pow(denom, p-2, p)) % p

p = 10 ** 9 + 7
n, a, b = map(int, input().split())
ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)


Fixed submission:
def cmb(n, r, p):
    r = min(r, n - r)
    res = 1
    for i in range(r):
        res *= pow(i+1, p-2, p)
        res *= n-i
        res %= p
    return res

p = 10 ** 9 + 7
n, a, b = map(int, input().split())
ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)

Buggy python submission (verdict: Time Limit Exceeded):
def cmb(n, r, p):
    r = min(r, n - r)
    res = 1
    for i in range(r):
        res *= pow(i+1, p-2, p)  # 分母の逆元
        res *= (n-i) % p  # 分子
    return res % p

p = 10 ** 9 + 7
n, a, b = map(int, input().split())
ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)


Fixed submission:
def cmb(n, r, p):
    r = min(r, n - r)
    res = 1
    for i in range(r):
        res *= pow(i+1, p-2, p)
        res *= n-i
        res %= p
    return res

p = 10 ** 9 + 7
n, a, b = map(int, input().split())
ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)

Buggy python submission (verdict: Time Limit Exceeded):
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 ** 6  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用

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)


n, a, b = map(int, input().split())
print(((2**n-1)%p - cmb(n, a, p) - cmb(n, b, p))%p)


Fixed submission:
def cmb(n, r, p):
    r = min(r, n - r)
    res = 1
    for i in range(r):
        res *= pow(i+1, p-2, p)
        res *= n-i
        res %= p
    return res

p = 10 ** 9 + 7
n, a, b = map(int, input().split())
ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)

Buggy python submission (verdict: Time Limit Exceeded):
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 ** 9  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用

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)

n, a, b = map(int, input().split())
ans = 2**n % p - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)


Fixed submission:
def cmb(n, r, p):
    r = min(r, n - r)
    res = 1
    for i in range(r):
        res *= pow(i+1, p-2, p)
        res *= n-i
        res %= p
    return res

p = 10 ** 9 + 7
n, a, b = map(int, input().split())
ans = pow(2, n, p) - 1
ans -= cmb(n, a, p) + cmb(n, b, p)
print(ans % p)