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)

def modpow(a, n, mod)
  exp = Math.log(n, 2).floor
  rep = modpow_cl(a, n, exp, mod)
  return rep[0]
end

def modpow_cl(a, n, exp, mod)
  if exp < 0
    rep = [1, a]
  else
    if n >= 2**exp
      rep = modpow_cl(a, n-2**exp, exp-1, mod)
      rep[0] = rep[0]*rep[1] % mod
    else
      rep = modpow_cl(a, n, exp-1, mod)
    end
    rep[1] = rep[1]**2 % mod
  end
  return rep
end

def modcomb(n, k, mod)
  return 1 if k < 1 || n <= k
  nume = deno = 1
  for i in 1..k
    nume = nume*(n-i+1) % mod
    deno = deno*i % mod
  end
  return nume*modpow(deno, mod-2, mod) % mod
end

N, A, B = gets.split.map(&:to_i)
MOD = 10**9+7

ans = modpow(2,N,MOD)-1-modcomb(N,A,MOD)-modcomb(N,B,MOD)
puts ans % MOD