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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

n, a, b = map(int, input().split())
mod = 10**9 + 7
ans = 0

f = 1
for i in range(1, n+1):
  f *= i
  f %= mod
     
# n!^-1 の計算
inv = pow(f, mod - 2, mod)
# n!^-1 - 1!^-1 の計算
invs = [1] * (n + 1)
invs[n] = inv
for m in range(n, 1, -1):
    inv *= m
    inv %= mod
    invs[m - 1] = inv

def comb(n,k):
  if k==0 or k==n: return 1
  return (f*invs[k]*invs[n-k])%mod

for i in range(1, n+1):
    if i != a and i != b:
        ans += (comb(n, i))
print(ans)