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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)


import java.util.*;
import static java.lang.System.*;
import java.io.*;
import java.math.*;

public class Main {
	static final long INF = 1000000007;
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		int a =sc.nextInt();
		int b =sc.nextInt();
		long cnt = 1;
		int m = n - 1;
		
		for (int i = 1; i <= m/2; i++) {
			cnt += combination(n, i) * 2;
			if (a == i) {
				cnt -= combination(n , i);
			}
			if(a == (n - 1))
				cnt -= combination(n , i);
			if (i == b) {
				cnt -= combination(n, i);
			}
			if(i == (n - b))
				cnt -= combination(n , i);
		}
		if (m % 2 == 1 && m/2+1 != a && m/2+1 !=b)
			cnt += combination(n , m/2+1);		
		if (n == a || n == b)
			cnt--;
		
		out.println(cnt % INF);
		
       out.close();
    }
	public static long factorial(long n) {
		if (n <= 1)
			return 1;
		else {
			return (n * factorial(n - 1)) % INF;
		}
	}

	public static long combination(long n, long r) {
		long top = n;
		for (int i = 0; i < r - 1; i++) {
			top = (top * (--n)) % INF;
		}
		long bottom = factorial(r);
		return top / bottom;
	}
	
static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}
}