Buggy python submission (verdict: Time Limit Exceeded):
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((2**n - 1 - cmb(n,a) - cmb(n,b)) % mod)

Fixed submission:
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)

Buggy python submission (verdict: Time Limit Exceeded):
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)

Fixed submission:
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)

Buggy python submission (verdict: Runtime Error):
    def cmb(n, r):
    	if n - r < r:
    		r = n - r
    	if r == 0:
    		return 1
    	if r == 1:
    		return n
    	
    	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
    	den = [k + 1 for k in range(r)] #denominator(分母)
    	
    	for p in range(2, r + 1):
    		pivot = den[p - 1]
    		if pivot > 1:
    			offset = (n - r) % p
    			for k in range(p - 1, r, p):
    				num[k - offset] /= pivot
    				den[k] /= pivot
    	
    	result = 1
    	for k in range(r):
    		if num[k] > 1:
    			result *= int(num[k])
    	
    	return result
     
    n,a,b = map(int,input().split())
     
    print((2**n - 1 - cmb(n,a) - cmb(n,b)) % (10**9 + 7))

Fixed submission:
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)

Buggy python submission (verdict: Runtime Error):
    n,a,b = map(int,input().split())
    mod = 10**9+7
     
    from math import factorial
    cmb_a = factorial(n) / factorial(a) / factorial(n-a)
    cmb_b = factorial(n) / factorial(b) / factorial(n-b)
     
    print(int((2**n - 1 - cmb_a - cmb_b) % mod))

Fixed submission:
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)

Buggy python submission (verdict: Time Limit Exceeded):
mod = 10**9 + 7
N = 10**9
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]

for i in range(2, N + 1):
	g1.append((g1[-1] * i) % mod)
	inverse.append((-inverse[mod % i] * (mod // i)) % mod)
	g2.append((g2[-1] * inverse[-1]) % mod)

def cmb(n, r, mod):
	if r < 0 or r > n:
		return 0
	r = min(r, n-r)
	return g1[n] * g2[r] * g2[n - r] % mod


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

#print(cmb(n,a) % mod)
#print(cmb(n,b) % mod)
print((2**n - 1 - cmb(n,a,mod) - cmb(n,b,mod)) % mod)

Fixed submission:
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)

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

# 有理数クラスをインポート
from fractions import Fraction

# 組合せの総数
def comb(n, k):
    
    if n < 0 or k < 0:
        pdt = 0
    
    else:
        pdt = 1
        for s in range(1, k + 1):
            pdt *= Fraction(n - s + 1, s)
    
    # 戻り値をint型にするために分子を取り出す
    return pdt.numerator

print((2**n - 1 - comb(n,a) - comb(n,b)) % mod)

Fixed submission:
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)

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

from math import factorial
cmb_a = factorial(n) / factorial(a) / factorial(n-a)
cmb_b = factorial(n) / factorial(b) / factorial(n-b)

print(int((2**n - 1 - cmb_a - cmb_b) % mod))

Fixed submission:
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)

Buggy python submission (verdict: Time Limit Exceeded):
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
	
	return result

n,a,b = map(int,input().split())

print((2**n - 1 - cmb(n,a) - cmb(n,b)) % (10**9 + 7))

Fixed submission:
def cmb(n, r):
	if n - r < r:
		r = n - r
	if r == 0:
		return 1
	if r == 1:
		return n
	
	num = [n - r + k + 1 for k in range(r)] #numerator(分子)
	den = [k + 1 for k in range(r)] #denominator(分母)
	
	for p in range(2, r + 1):
		pivot = den[p - 1]
		if pivot > 1:
			offset = (n - r) % p
			for k in range(p - 1, r, p):
				num[k - offset] /= pivot
				den[k] /= pivot
	
	result = 1
	for k in range(r):
		if num[k] > 1:
			result *= int(num[k])
			result = result % mod
	
	return result

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

print((pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)) % mod)