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).

Solution in Ruby (2.3.3) (judge verdict: Accepted)

MOD = 10 ** 9 + 7
MAX = 2 * 10 ** 5

def comb(n, k)
  npk = 1
  k.times do |i|
    npk = (npk * (n - i)) % MOD
  end
 
  k_x = 1
  k.downto(1) do |i|
    k_x = (k_x * i) % MOD
  end
  (npk * mod_inv(k_x, MOD)) % MOD
end

def mod_inv(a, m)
  b = m
  u = 1
  v = 0 
  while b != 0
    t = a / b
    a -= t * b;
    tmp = a
    a = b
    b = tmp
 
    u -= t * v
    tmp = u
    u = v
    v = tmp
  end
 
  u = u % m
  if u < 0
    u += m
  end
  return u
end

def modpow(a, n)
  res = 1
  while n > 0
    res = res * a % MOD if n & 1 == 1
    a = a * a % MOD
    n >>= 1
  end
  res
end

  
N, A, B = gets.split.map(&:to_i)


ans = (modpow(2, N) - 1) % MOD
[A, B].each do |kk|
  ans -= comb(N, kk)
end

p ans % MOD