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

def pow(x, n, mod = 10 ** 9 + 7)
  return 1 if n == 0
  return pow(x**2 % mod, n / 2, mod) if (n % 2) == 0
  return pow(x**2 % mod, n / 2, mod) * x % mod if (n % 2) == 1
end

# Permutation: n * (n-1) * …… * (n-k+1) (mod p); O(k)
def prm(n, k, m = 10**9+7)
  (0...k).inject(1){|res,i| res * (n-i) % m }
end

# combination: nPk / k! (mod p), note: p must be a prime number
def cmb(n, k, m = 10**9+7)
  k = n - k if k > n - k
  return prm( n, k, m ) * pow( prm(k, k), m-2, m ) % m
end

n,a,b = gets.split.map(&:to_i)

#何も選ばない1通りを除く
ans = pow(2,n,mod) - 1 - cmb(n,a) - cmb(n,b)
ans %= mod

puts ans