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

M = pow(2, N,m)

m = 10**9+7
#互いに素なa,bについて、a*x+b*y=1の一つの解
def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m
  

res = 1
for i in range(N-a+1,N+1):
    res = res*i%m
for i in range(1,a+1):
    res = res*mod_inv(i,m)%m

rs = 1
for i in range(N-b+1,N+1):
    rs = rs*i%m
for i in range(1,b+1):
    rs = rs*mod_inv(i,m)%m

print((M-1-res-rs)%m)


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

M = pow(2, N, m)

def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)

Buggy python submission (verdict: Time Limit Exceeded):
N,a,b=map(int,input().split())
m = 10**9+7
def pow(x, n):
    ans = 1
    while n:
        if n % 2:
            ans *= x
            ans %= m
        x *= x
        n >>= 1
    return ans

M = pow(2, N)%m

m = 10**9+7
#互いに素なa,bについて、a*x+b*y=1の一つの解
def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m
  

res = 1
for i in range(N-a+1,N+1):
    res = res*i%m
for i in range(1,a+1):
    res = res*mod_inv(i,m)%m

rs = 1
for i in range(N-b+1,N+1):
    rs = rs*i%m
for i in range(1,b+1):
    rs = rs*mod_inv(i,m)%m

print(M-1-res-rs)


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

M = pow(2, N, m)

def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)

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

M = pow(2, N)%m

m = 10**9+7
#互いに素なa,bについて、a*x+b*y=1の一つの解
def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m
 
def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)

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

M = pow(2, N, m)

def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)

Buggy python submission (verdict: Time Limit Exceeded):
N,a,b=map(int,input().split())
m = 10**9+7
def pow(x, n):
    ans = 1
    while n:
        if n % 2:
            ans *= x
        x *= x
        n >>= 1
    return ans

M = pow(2, N)%m

m = 10**9+7
#互いに素なa,bについて、a*x+b*y=1の一つの解
def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m
  

res = 1
for i in range(N-a+1,N+1):
    res = res*i%m
for i in range(1,a+1):
    res = res*mod_inv(i,m)%m

rs = 1
for i in range(N-b+1,N+1):
    rs = rs*i%m
for i in range(1,b+1):
    rs = rs*mod_inv(i,m)%m

print(M-1-res-rs)

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

M = pow(2, N, m)

def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)

Buggy python submission (verdict: Time Limit Exceeded):
N,a,b=map(int,input().split())
m = 10**9+7
def pow(x, n):
    ans = 1
    while n:
        if n % 2:
            ans *= x
        x *= x
        n >>= 1
    return ans

M = pow(2, N)%m

#互いに素なa,bについて、a*x+b*y=1の一つの解
def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m
  
res = 1
for i in range(1,N+1):
    res = res*i%m
for i in range(1,N-a+1):
    res = res*mod_inv(i,m)%m
for i in range(1,a+1):
    res = res*mod_inv(i,m)%m

rs = 1
for i in range(1,N+1):
    rs = rs*i%m
for i in range(1,N-b+1):
    rs = rs*mod_inv(i,m)%m
for i in range(1,b+1):
    rs = rs*mod_inv(i,m)%m

print(M-1-res-rs)

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

M = pow(2, N, m)

def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)

Buggy python submission (verdict: Time Limit Exceeded):
import math

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

def pow(x, n):
    ans = 1
    while n:
        if n % 2:
            ans *= x
        x *= x
        n >>= 1
    return ans

M = pow(2, N)

c=1
d=1
for i in range(a):
  c*=(N-i)
  d*=i+1

e=1
f=1
for i in range(b):
  e*=(N-i)
  f*=i+1

print((M-1-c//d-e//f)%(10**9+7))

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

M = pow(2, N, m)

def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)

Buggy python submission (verdict: Time Limit Exceeded):
import math

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

def combinations_count(s, r):
    return math.factorial(s) // (math.factorial(s - r) * math.factorial(r))

p = combinations_count(n, a)
q = combinations_count(n, b)

print((2**n-1-p-q)%(10**9+7))

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

M = pow(2, N, m)

def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)

Buggy python submission (verdict: Time Limit Exceeded):
import math

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

def combinations_count(s, r):
    return math.factorial(s) // (math.factorial(s - r) * math.factorial(r))

p = combinations_count(n, a)
q = combinations_count(n, b)

print(2**n-1-p-q)

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

M = pow(2, N, m)

def nCr(n,r):
    if r*2>n:
        return nCr(n,n-r)
    else:
        a = b = 1
        for i in range(r):
            a = a * (n - i) % m
            b = b * (r - i) % m
        return (a * pow(b,m-2,m)) % m
 
ans = M - 1 - nCr(N,a) - nCr(N,b)
print(ans%m)