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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

# coding: utf-8
def modpow(x, n, mod):
    if n == 0:
        return 1
    elif n % 2 == 0:
        return modpow((x**2) % mod, n // 2, mod)
    else:
        return x * modpow(x, n - 1, mod) % mod
def modcomb(n, r, mod):
    "nCr = X/Yとおく"
    r = min(r, n - r)
    ue, sita = 1, 1
    for i in range(1, r + 1):
        ue *= (n + 1 - i) % mod
        sita *= i % mod
    # return ue * modpow(sita, mod-2, mod)
    return ue * pow(sita, mod-2, mod)

N, A, B = map(int, input().split())
mod = 10 ** 9 + 7

ans = pow(2, N, mod) - 1
ans -= modcomb(N, A, mod)
# ans -= cmb(N, A, mod) % mod
ans %= mod
ans -= modcomb(N, B, mod)
# ans -= cmb(N, B, mod) % mod
ans %= mod
print(ans % mod)