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: Runtime Error)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.NoSuchElementException;

public class Main {

	static long[] fac;
	static long[] inv;
	static long[] finv;
	static final int mod = 1000000007;

	public static void main(String[] args) {

		long mod = 1000 * 1000 * 1000 + 7;

		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);

		long N = sc.nextLong();
		int A = sc.nextInt();
		int B = sc.nextInt();
		long oldN=N;
		calcNumOfCombinationInit((int)N + 1);


		ArrayList<Long> twos = new ArrayList<Long>();
		twos.add(1L);
		for (int i = 1; i <= 30; i++) {
			twos.add(twos.get(i - 1) * 2);
		}

		ArrayList<Long> amari = new ArrayList<Long>();
		amari.add(2L);
		for (int i = 1; i < 30; i++) {
			amari.add((amari.get(i - 1) * amari.get(i - 1)) % mod);
		}

		long ans = 1;
		for (int i = 30; i >= 0; i--) {
			if (N >= twos.get(i)) {
				N = N - twos.get(i);
				ans = (ans * amari.get(i)) % mod;
			}
		}

		long combA = calcNumOfCombination((int)oldN, A);
		long combB = calcNumOfCombination((int)oldN, A);


		out.print((ans-combA-combB-1)%mod);
		out.flush();
	}

	static long lcm(long a, long b) {
		long temp;
		long c = a;
		c *= b;
		while ((temp = a % b) != 0) {
			a = b;
			b = temp;
		}
		return (c / b);
	}

	static void calcNumOfCombinationInit(int N) {

		fac = new long[N];
		inv = new long[N];
		finv = new long[N];
		fac[0] = 1;
		fac[1] = 1;
		finv[0] = 1;
		finv[1] = 1;
		inv[1] = 1;
		for (int i = 2; i < N; i++) {
			fac[i] = fac[i - 1] * i % mod;
			inv[i] = mod - inv[mod % i] * (mod / i) % mod;
			finv[i] = finv[i - 1] * inv[i] % mod;
		}
	}

	static long calcNumOfCombination(int n, int r) {
		if (n < r || n < 0 || r < 0) {
			return 0;
		}
		return fac[n] * (finv[r] * finv[n - r] % mod) % mod;
	}

}

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());
	}

	public int[] nextIntsN(int N) {
		int[] ints = new int[N];
		for (int i = 0; i < N; i++) {
			ints[i] = nextInt();
		}
		return ints;
	}

	public long[] nextLongsN(int N) {
		long[] longs = new long[N];
		for (int i = 0; i < N; i++) {
			longs[i] = nextLong();
		}
		return longs;
	}

	public char[] nextCharsN(int N) {
		char[] chars = new char[N];
		String msg = next();
		for (int i = 0; i < N; i++) {
			chars[i] = msg.charAt(i);
		}
		return chars;
	}

	public char[][] nextCharsHW(int H, int W) {
		char[][] chars = new char[H][W];
		for (int i = 0; i < H; i++) {
			String str = next();
			for (int j = 0; j < W; j++) {
				chars[i][j] = str.charAt(j);
			}
		}
		return chars;
	}

	public int[][] nextIntsNM(int N, int M) {
		int[][] ints = new int[N][M];
		for (int i = 0; i < N; i++) {
			for (int j = 0; j < M; j++) {
				ints[i][j] = nextInt();
			}
		}
		return ints;
	}

	public List<Integer> nextArrayIntsN(int N) {
		ArrayList<Integer> array = new ArrayList<>(N);
		for (int i = 0; i < N; i++) {
			array.add(nextInt());
		}
		return array;
	}

	public List<Long> nextArrayLongsN(int N) {
		ArrayList<Long> array = new ArrayList<>(N);
		for (int i = 0; i < N; i++) {
			array.add(nextLong());
		}
		return array;
	}

	public List<List<Long>> nextArrayLongsNM(int N, int M) {

		List<List<Long>> arrays = new ArrayList<List<Long>>(M);
		for (int i = 0; i < M; i++) {
			List<Long> array = nextArrayLongsN(N);
			arrays.add(array);
		}
		return arrays;
	}

}