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)

import sys, re, os
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
# from fractions import gcd
from itertools import permutations, combinations, product, accumulate
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from functools import reduce
from bisect import bisect_left, insort_left
from heapq import heapify, heappush, heappop

INPUT = lambda: sys.stdin.readline().rstrip()
INT = lambda: int(INPUT())
MAP = lambda: map(int, INPUT().split())
S_MAP = lambda: map(str, INPUT().split())
LIST = lambda: list(map(int, INPUT().split()))
S_LIST = lambda: list(map(str, INPUT().split()))

sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

N, A, B = MAP()


def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod


g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]

for i in range( 2, N + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )


def main():
    ans = 0
    for i in range(N):
        if i+1 == A or i+1 == B: continue
        ans += cmb(N, i+1, mod)

    print(ans)


if __name__ == '__main__':
    main()