Problem:


Score : 400 points

Problem Statement

Akari has n kinds of flowers, one of each kind.

She is going to choose one or more of these flowers to make a bouquet.

However, she hates two numbers a and b, so the number of flowers in the bouquet cannot be a or b.

How many different bouquets are there that Akari can make?

Find the count modulo (10^9 + 7).

Here, two bouquets are considered different when there is a flower that is used in one of the bouquets but not in the other bouquet.

Constraints

All values in input are integers.

2 \leq n \leq 10^9

1 \leq a < b \leq \textrm{min}(n, 2 \times 10^5)

Input

Input is given from Standard Input in the following format:

n a b

Output

Print the number of bouquets that Akari can make, modulo (10^9 + 7). (If there are no such bouquets, print 0.)

Sample Input 1

4 1 3

Sample Output 1

7

In this case, Akari can choose 2 or 4 flowers to make the bouquet.

There are 6 ways to choose 2 out of the 4 flowers, and 1 way to choose 4, so there are a total of 7 different bouquets that Akari can make.

Sample Input 2

1000000000 141421 173205

Sample Output 2

34076506

Print the count modulo (10^9 + 7).



Sample input:
4 1 3


Sample output:
7

Submission status: Accepted

Solution code:
MOD = int (1e9) + 7
STEP = 1000000

sec = [1, 128233642, 993191796, 246084337, 175673566, 883787401, 470931556, 119995528, 225567908, 757928892, 250015370, 
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825454299, 183907026, 881797659, 823559228, 703904407, 624713517, 805011386, 175293956, 157911929, 315160646, 59387184, 711105445, 710926865, 239798930, 734168782, 513146799, 71626953, 883937988, 613778426, 107738376, 960564286, 84887701, 771212964, 71595332, 319321717, 980960223, 368173468, 67320689, 862499851, 864972828, 48646097, 670160814, 725736339, 790163830, 663423088, 255691818, 388742192, 305094892, 522669454, 472392039, 946047214, 445919328, 
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n, a, b = list (map (int, input().split()))

ans = 1

def fastPower (a, k) :
    res = 1
    base = a % MOD
    while (k) :
        if (k & 1) :
            res = res * base % MOD
        base = base * base % MOD
        k >>= 1
    return res

ans = (fastPower (2, n) - 1 + MOD) % MOD

def fac (x) :
    if (x == 0) :
        return 1
    k = x // STEP
    res = sec[k] % MOD
    for i in range (k * STEP, x + 1) :
        if (i == 0) :
            continue
        res = res * i % MOD
    return res

def C (n, m) :
    if (n < m) :
        return -1
    f1 = fac (m)
    f2 = fac (n - m)
    return ((fac (n) * fastPower (f1, MOD - 2)) % MOD * fastPower (f2, MOD - 2) % MOD)

print ((ans + MOD - C (n, a) - C (n, b) + MOD) % MOD)

Submission status: Accepted

Solution code:
import math

# 高速冪乗計算

def fast_modexp(x, e, n=(10**9+7)):
    y = 1
    for k in range(e.bit_length()):
        if e & (1<<(e.bit_length()-k-1)):
            y = y * y * x % n
        else:
            y = y * y % n

    return y

n, a, b = map(int, input().split())
numer_a = 1
numer_b = 1
for i in range(a):
    numer_a = (numer_a * (n-i)) % (10**9+7)

for i in range(b):
    numer_b = (numer_b * (n-i)) % (10**9+7)

denom_a = 1
denom_b = 1

for i in range(1, a+1):
    denom_a = (denom_a * i) % (10**9+7)

for i in range(1, b+1):
    denom_b = (denom_b * i) % (10**9+7)

ans = fast_modexp(2, n)
ans = (ans - 1) % (10**9+7)
ans = (ans - numer_a * fast_modexp(denom_a, 10**9+5)) % (10**9+7)
ans = (ans - numer_b * fast_modexp(denom_b, 10**9+5)) % (10**9+7)


print(ans)

Submission status: Accepted

Solution code:
MOD = 10**9 + 7
class ModInt:
    def __init__(self, x):
        self.x = x % MOD

    def __str__(self):
        return str(self.x)

    __repr__ = __str__

    def __add__(self, other):
        return (
            ModInt(self.x + other.x) if isinstance(other, ModInt) else
            ModInt(self.x + other)
        )

    def __sub__(self, other):
        return (
            ModInt(self.x - other.x) if isinstance(other, ModInt) else
            ModInt(self.x - other)
        )

    def __mul__(self, other):
        return (
            ModInt(self.x * other.x) if isinstance(other, ModInt) else
            ModInt(self.x * other)
        )

    def __truediv__(self, other):
        return (
            ModInt(
                self.x * pow(other.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(self.x * pow(other, MOD - 2, MOD))
        )

    def __pow__(self, other):
        return (
            ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(self.x, other, MOD))
        )

    __radd__ = __add__

    def __rsub__(self, other):
        return (
            ModInt(other.x - self.x) if isinstance(other, ModInt) else
            ModInt(other - self.x)
        )

    __rmul__ = __mul__

    def __rtruediv__(self, other):
        return (
            ModInt(
                other.x * pow(self.x, MOD - 2, MOD)
            ) if isinstance(other, ModInt) else
            ModInt(other * pow(self.x, MOD - 2, MOD))
        )

    def __rpow__(self, other):
        return (
            ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else
            ModInt(pow(other, self.x, MOD))
        )

def cmb(fact, n, r):
    mul = ModInt(1)
    for i in range(n - r + 1, n + 1):
        mul *= i
    return mul / fact[r]

def solve(n, a, b):
    fact = [ModInt(1)]
    for i in range(1, max(a, b) + 1):
        fact.append(fact[i-1] * i)
    return  ModInt(pow(2,n)) - 1 - cmb(fact, n, a) - cmb(fact, n, b)

if __name__ == '__main__':
    n, a, b = map(int, input().split())
    ret = solve(n, a, b)
    print(ret)

Submission status: Accepted

Solution code:
n, a, b = map(int, input().split())
def mod_comb(n, r, mod):
    ans = 1
    for i in range(1, r + 1):
        ans *= n - (i - 1)
        ans %= mod
        ans *= inv[i]
        ans %= mod
    return int(ans)
p = 10 ** 9 + 7
N = 10 ** 6  # N は必要分だけ用意する
fact = [1, 1]
factinv = [1, 1]
inv = [0, 1]
 
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)
import math
mod = 10 ** 9 + 7
res = pow(2, n, mod) - 1 - mod_comb(n, a, mod) - mod_comb(n, b, mod)
print(res % mod)

Submission status: Accepted

Solution code:
class Comb0():
    # あらかじめO(k)の前計算をしておいてr<=kに対してnCrを高速に計算する
    def __init__(self, n, k=10**6, p=10**9+7):
        # num[i]=nPi
        # den[i]=(i!)^(-1)
        num, den = [1], [1]
        a, b = 1, 1
        for i in range(1, k+1):
            a = (a*(n-i+1)) % p
            b = (b*pow(i, p-2, p)) % p
            num.append(a)
            den.append(b)
        self.num = num
        self.den = den
        self.n = n
        self.p = p

    def calc(self, r):
        num, den = self.num, self.den
        if r < 0 or self.n < r:
            return 0
        return (num[r] * den[r]) % self.p


n, a, b = map(int, input().split())
p = 10**9+7
cmb = Comb0(n, k=max(a, b))
print((pow(2, n, p)-1-cmb.calc(a)-cmb.calc(b)) % p)

Submission status: Accepted

Solution code:
INT_MAX=10**18+7
x=10**9+7
def INPUT():return list(int(i) for i in input().split())
def LIST_1D_ARRAY(n):return [0 for _ in range(n)]
def LIST_2D_ARRAY(m,n):return [[0 for _ in range(n)]for _ in range(m)]
GETA=123
###############################################################################
import math as M
n,a,b=INPUT()
#ans=2^n-1-(n,a)-(n,b)
def power(a,n):
    if n==0:
        return 1
    else:
        if(n%2==0):
            return ((power(a,n//2))**2)%x
        else:
            return ((a%x)*(((power(a,(n-1)//2)))**2)%x)%x
def bin(n,r):
    num=1
    den=1
    for i in range(1,r+1):
        den=(den*i)%x
        num=(num*(n-i+1))%x
    return (num*power(den,x-2))%x
ans=power(2,n)-1-bin(n,a)-bin(n,b)
if ans>0:
    print(ans)
else:
    print((x+ans)%x)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

def table(n:int, p=10**9+7):
    global fact, factinv, inv
    fact = [1, 1]
    factinv = [1, 1]
    inv = [0, 1]
    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)

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)
table(N)

mca = bunshi= 1
for i in range(1, a+1):
    #mca *= (m-i+1) * inv[i]
    mca *= (m-i+1)
    bunshi *= i 
    mca %= P
    bunshi %= P
mcb = mca
mca = mca * pow(bunshi, P-2, P)
mca %= P

for i in range(a+1, b+1):
    #mcb *= (m-i+1) * inv[i]
    mcb *= (m-i+1)
    bunshi *= i 
    mcb %= P
    bunshi %= P
mcb = mcb * pow(bunshi, P-2, P)
mcb %= P

print((pow(2, m, P)-1-mca-mcb) % P)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

# 繰り返し二乗法
def pow_r_mod(x:int, n:int, mod=10**9+7)->int:
    # 計算量 : log N
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        x %= mod
        n //= 2
    return (K * x) % mod

def table(n:int, p=10**9+7):
    global fact, factinv, inv
    fact = [1, 1]
    factinv = [1, 1]
    inv = [0, 1]
    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)

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)
table(N)

mca = 1
for i in range(1, a+1):
    mca *= (m-i+1) * inv[i]
    mca %= P

mcb = mca
for i in range(a+1, b+1):
    mcb *= (m-i+1) * inv[i]
    mcb %= P

print((pow_r_mod(2, m)-1-mca-mcb) % P)
#print((pow(2, m, P)-1-mca-mcb) % P)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

# 繰り返し二乗法
def pow_r_mod(x:int, n:int, mod=10**9+7)->int:
    # 計算量 : log N
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        x %= mod
        n //= 2
    return (K * x) % mod

def table(n:int, p=10**9+7):
    global fact, factinv, inv
    fact = [1, 1]
    factinv = [1, 1]
    inv = [0, 1]
    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)

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)
table(N)

mca = 1
for i in range(1, a+1):
    mca *= (m-i+1) * inv[i]
    mca %= P

mcb = mca
for i in range(a+1, b+1):
    mcb *= (m-i+1) * inv[i]
    mcb %= P

#print((pow_r_mod(2, m)-1-mca-mcb) % P)
print((pow(2, m, P)-1-mca-mcb) % P)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

# 繰り返し二乗法
def pow_r_mod(x:int, n:int, mod=10**9+7)->int:
    # 計算量 : log N
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        x %= mod
        n //= 2
    return (K * x) % mod

def table(n:int, p=10**9+7):
    global fact, factinv, inv
    fact = [1, 1]
    factinv = [1, 1]
    inv = [0, 1]
    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)

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)
table(N)

mca = 1
for i in range(1, a+1):
    mca *= (m-i+1) * inv[i]
    mca %= P

mcb = mca
for i in range(a+1, b+1):
    mcb *= (m-i+1) * inv[i]
    mcb %= P

print((pow_r_mod(2, m)-1-mca-mcb) % P)

Submission status: Accepted

Solution code:
#設定
import sys
input = sys.stdin.buffer.readline

#ライブラリインポート
from collections import defaultdict

con = 10 ** 9 + 7
#入力受け取り
def getlist():
	return list(map(int, input().split()))

#処理内容
def main():
	N, A, B = getlist()
	ans = pow(2, N, con) - 1

	dif = 1
	var = N
	for i in range(A):
		inv = pow((1 + i) , con - 2, con)
		dif = dif * (var - i) * inv
		dif %= con
	ans -= dif
	dif = 1
	for i in range(B):
		inv = pow((1 + i) , con - 2, con)
		dif = dif * (var - i) * inv
		dif %= con
	ans -= dif

	ans %= con
	print(ans)

if __name__ == '__main__':
	main()

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

# 繰り返し二乗法
def pow_r_mod(x:int, n:int, mod=10**9+7)->int:
    # 計算量 : log N
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        x %= mod
        n //= 2
    return (K * x) % mod

def table(n:int, p=10**9+7):
    global fact, factinv, inv
    fact = [1, 1]
    factinv = [1, 1]
    inv = [0, 1]
    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)

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)
#inv_t = [0]+[1]
# 逆元
#for i in range(2, N):
  #inv_t += [inv_t[P % i] * (P - int(P / i)) % P]
table(N)

mca = 1
for i in range(1, a+1):
    mca *= (m-i+1) * inv[i]
    mca %= P

mcb = mca
for i in range(a+1, b+1):
    mcb *= (m-i+1) * inv[i]
    mcb %= P

print((pow_r_mod(2, m)-1-mca-mcb) % P)
#print((mod_pow(2, m, P)-1-mca-mcb) % P)

Submission status: Accepted

Solution code:
#!/usr/bin python3
# -*- coding: utf-8 -*-

import sys
input = sys.stdin.readline

def nCr(n, r, mod):
    ret = [1]*(r+1)
    for i in range(1, r+1):
        ret[i] = (ret[i-1] * (n-i+1) * pow(i,mod-2,mod)) % mod
    return ret

def main():
    n, a, b = map(int, input().split())
    mod = 10**9+7
#すべて
    ret = pow(2, n, mod)-1
#a,bの場合
    nCrsq = nCr(n, b, mod)
    ret -= nCrsq[b]
    ret -= nCrsq[a]

    print(ret%mod)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

# 繰り返し二乗法
def pow_r_mod(x:int, n:int, mod=10**9+7)->int:
    # 計算量 : log N
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        x %= mod
        n //= 2
    return (K * x) % mod

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)+1
inv_t = [0]+[1]
# 逆元
for i in range(2, N):
  inv_t += [inv_t[P % i] * (P - int(P / i)) % P]

mca = mcb = 1

for i in range(1, a+1):
    mca *= (m-i+1) * inv_t[i]
    mca %= P

mcb = mca

for i in range(a+1, b+1):
    mcb *= (m-i+1) * inv_t[i]
    mcb %= P

print((pow_r_mod(2, m)-1-mca-mcb) % P)
#print((mod_pow(2, m, P)-1-mca-mcb) % P)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

def pow_r_mod(x:int, n:int, mod=10**9+7)->int:
    # 計算量 : log N
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        x %= mod
        n //= 2
    return (K * x) % mod

def  mod_pow(a:int, b:int, mod:int)->int:
    if b % 2 == 0:
        return (mod_pow(a, b//2, mod) ** 2) % mod
    elif b == 1:
        return a % mod
    else:
        return ((mod_pow(a, b//2, mod) ** 2) * a) % mod

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)+1
inv_t = [0]+[1]
for i in range(2, N):
  inv_t += [inv_t[P % i] * (P - int(P / i)) % P]

mca = mcb = 1

for i in range(1, a+1):
    mca *= (m-i+1) * inv_t[i]
    mca %= P

for i in range(1, b+1):
    mcb *= (m-i+1) * inv_t[i]
    mcb %= P

print((pow_r_mod(2, m)-1-mca-mcb) % P)
#print((mod_pow(2, m, P)-1-mca-mcb) % P)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

def pow_r_mod(x, n, mod=10**9+7):
    # 計算量 : log N
    if n == 0:
        return 1
    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        x %= mod
        n //= 2
    return (K * x) % mod

def  mod_pow(a:int, b:int, mod:int)->int:
    if b % 2 == 0:
        return (mod_pow(a, b//2, mod) ** 2) % mod
    elif b == 1:
        return a % mod
    else:
        return ((mod_pow(a, b//2, mod) ** 2) * a) % mod

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)+1
inv_t = [0]+[1]
for i in range(2, N):
  inv_t += [inv_t[P % i] * (P - int(P / i)) % P]

mca = mcb = 1

for i in range(1, a+1):
    mca *= (m-i+1) * inv_t[i]
    mca %= P

for i in range(1, b+1):
    mcb *= (m-i+1) * inv_t[i]
    mcb %= P

#print((pow_r_mod(2, m)-1-mca-mcb) % P)
print((mod_pow(2, m, P)-1-mca-mcb) % P)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for _ in range(N)]
def dp2(ini, i, j): return [[ini]*i for _ in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for _ in range(j)] for _ in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
#from itertools import accumulate #list(accumulate(A))

def pow_r_mod(x, n, mod=10**9+7):
    """
    O(log n)
    """
    if n == 0:
        return 1

    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        x %= mod
        n //= 2

    return (K * x) % mod

m, a, b = mi()

P = 10**9+7
N = 2*(10**5)+1
inv_t = [0]+[1]
for i in range(2,N):
  inv_t += [inv_t[P % i] * (P - int(P / i)) % P]

mca = mcb = 1

for i in range(1, a+1):
    mca *= (m-i+1) * inv_t[i]
    mca %= P

for i in range(1, b+1):
    mcb *= (m-i+1) * inv_t[i]
    mcb %= P

print((pow_r_mod(2, m)-1-mca-mcb) % P)