There are n lights aligned in a row. These lights are numbered 1 to n from left to right. Initially some of the lights are switched on. Shaass wants to switch all the lights on. At each step he can switch a light on (this light should be switched off at that moment) if there's at least one adjacent light which is already switched on. 

He knows the initial state of lights and he's wondering how many different ways there exist to switch all the lights on. Please find the required number of ways modulo 1000000007 (109 + 7).

Input

The first line of the input contains two integers n and m where n is the number of lights in the sequence and m is the number of lights which are initially switched on, (1 ≤ n ≤ 1000, 1 ≤ m ≤ n). The second line contains m distinct integers, each between 1 to n inclusive, denoting the indices of lights which are initially switched on.

Output

In the only line of the output print the number of different possible ways to switch on all the lights modulo 1000000007 (109 + 7).

Examples

Input

3 1
1


Output

1


Input

4 2
1 4


Output

2


Input

11 2
4 8


Output

6720
import java.io.BufferedInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.Random;
import java.util.Set;
import java.util.SortedSet;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main
{	
	/********************************************** a list of common variables **********************************************/
	private MyScanner scan = new MyScanner();
	private PrintWriter out = new PrintWriter(System.out);
	private final double PI = Math.acos(-1.0);
	private final int SIZEN = (int)(1e5);
	private final long MOD = (int)(1e9 + 7);
	private final long MODH = 10000000007L, BASE = 10007;
	private final int[] DX = {0, 1, 0, -1}, DY = {-1, 0, 1, 0};
	private ArrayList<Integer>[] edge;	
	
	public void foo()
	{
		int n = scan.nextInt();
		int m = scan.nextInt();
		int[] a = new int[m];
		for(int i = 0;i < m;++i)
		{
			a[i] = scan.nextInt();
		}
		Arrays.sort(a);
		long x = 1;
		for(int i = 1;i <= n - m;++i)
		{
			x = x * i % MOD;
		}
		long y = 1;
		for(int i = 1;i < a[0];++i)
		{
			y = y * i % MOD;
		}
		for(int i = 0;i < m - 1;++i)
		{
			for(int j = 1;j < a[i + 1] - a[i] - 1;++j)
			{
				y = y * j % MOD;
				x = x * 2 % MOD;
			}
			if(a[i + 1] > a[i] + 1)
			{
				y = y * (a[i + 1] - a[i] - 1) % MOD;
			}
		}
		for(int i = 1;i <= n - a[m - 1];++i)
		{
			y = y * i % MOD;
		}
		y = quickMod(y, MOD - 2);
		long ans = x * y % MOD;
		out.println(ans);
	}

	public static void main(String[] args)
	{
		Main m = new Main();
		m.foo();
		m.out.close();
	}
	
	/********************************************** a list of common algorithms **********************************************/
	/**
	 * 1---Get greatest common divisor
	 * @param a :	first number
	 * @param b :	second number
	 * @return		greatest common divisor
	 */
	public long gcd(long a, long b)
	{
		return 0 == b ? a : gcd(b, a % b);
	}
	
	/**
	 * 2---Get the distance from a point to a line
	 * @param x1	the x coordinate of one endpoint of the line
	 * @param y1	the y coordinate of one endpoint of the line
	 * @param x2	the x coordinate of the other endpoint of the line
	 * @param y2	the y coordinate of the other endpoint of the line
	 * @param x		the x coordinate of the point 
	 * @param y		the x coordinate of the point
	 * @return		the distance from a point to a line
	 */
	public double getDist(long x1, long y1, long x2, long y2, long x, long y)
	{
		long a = y2 - y1;
		long b = x1 - x2;
		long c = y1 * (x2 - x1) - x1 * (y2 - y1);
		return Math.abs(a * x + b * y + c) / Math.sqrt(a * a + b * b);
	}
	
	/**
	 * 3---Get the distance from one point to a segment (not a line)
	 * @param x1	the x coordinate of one endpoint of the segment
	 * @param y1	the y coordinate of one endpoint of the segment
	 * @param x2	the x coordinate of the other endpoint of the segment
	 * @param y2	the y coordinate of the other endpoint of the segment
	 * @param x		the x coordinate of the point
	 * @param y		the y coordinate of the point
	 * @return		the distance from one point to a segment (not a line)
	 */
	public double ptToSeg(long x1, long y1, long x2, long y2, long x, long y)
	{
		double cross = (x2 - x1) * (x - x1) + (y2 - y1) * (y - y1);
		if(cross <= 0)
		{
			return (x - x1) * (x - x1) + (y - y1) * (y - y1);
		}
		double d = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
		if(cross >= d) 
		{
			return (x - x2) * (x - x2) + (y - y2) * (y - y2);
		}
		double r = cross / d;
		double px = x1 + (x2 - x1) * r;
		double py = y1 + (y2 - y1) * r;
		return (x - px) * (x - px) + (y - py) * (y - py);
	}
	
	/**
	 * 4---KMP match, i.e. kmpMatch("abcd", "bcd") = 1, kmpMatch("abcd", "bfcd") = -1.
	 * @param t:	String to match.
	 * @param p:	String to be matched.
	 * @return		if can match, first index; otherwise -1.
	 */
	public int kmpMatch(char[] t, char[] p)
	{
		int n = t.length;
		int m = p.length;
		int[] next = new int[m + 1];
		next[0] = -1;
		int j = -1;
		for(int i = 1;i < m;++i)
		{
			while(j >= 0 && p[i] != p[j + 1])
			{
				j = next[j];
			}
			if(p[i] == p[j + 1])
			{
				++j;
			}
			next[i] = j;
		}
		j = -1;
		for(int i = 0;i < n;++i)
		{
			while(j >= 0 && t[i] != p[j + 1])
			{
				j = next[j];
			}
			if(t[i] == p[j + 1])
			{
				++j;
			}
			if(j == m - 1)
			{
				return i - m + 1;
			}
		}
		return -1;
	}
	
	/**
	 * 5---Get the hash code of a String
	 * @param	s:	input string
	 * @return	hash code
	 */
	public long hash(String s)
	{
		long key = 0, t = 1;
		for(int i = 0;i < s.length();++i)
		{
			key = (key + s.charAt(i) * t) % MODH;
			t = t * BASE % MODH;
		}
		return key;
	}
	
	/**
	 * 6---Get x ^ n % MOD quickly.
	 * @param	x:	base
	 * @param 	n:	times
	 * @return	x ^ n % MOD
	 */
	public long quickMod(long x, long n)
	{
		long ans = 1;
		while(n > 0)
		{
			if(1 == n % 2)
			{
				ans = ans * x % MOD;
 			}
			x = x * x % MOD;
			n >>= 1;
		}
		return ans;
	}
	
	class MyScanner
	{
	    private byte[] buf = new byte[1024];
	    private int curChar;
	    private int numChars;
	    BufferedInputStream bis = new BufferedInputStream(System.in);

	    public int read() 
	    {
	        if (-1 == numChars)
	        {
	        	throw new InputMismatchException();
	        }
	        if (curChar >= numChars)
	        {
	            curChar = 0;
	            try 
	            {
	                numChars = bis.read(buf);
	            }
	            catch (IOException e)
	            {
	                throw new InputMismatchException();
	            }
	            if (numChars <= 0)
	            {
	            	return -1;
	            }
	        }
	        return buf[curChar++];
	    }

	    public int nextInt() 
	    {
	        int c = read();
	        while (isSpaceChar(c))
	        {
	        	c = read();
	        }
	        int sgn = 1;
	        if (c == '-') 
	        {
	            sgn = -1;
	            c = read();
	        }
	        int res = 0;
	        do 
	        {
	            if (c < '0' || c > '9')
	            {
	            	throw new InputMismatchException();
	            }
	            res *= 10;
	            res += c - '0';
	            c = read();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }
	    
	    public long nextLong() 
	    {
	    	int c = read();
	    	while (isSpaceChar(c))
	    	{
	    		c = read();
	    	}
	    	int sgn = 1;
	    	if (c == '-') 
	    	{
	    		sgn = -1;
	    		c = read();
	    	}
	    	long res = 0;
	    	do 
	    	{
	    		if (c < '0' || c > '9')
	    		{
	    			throw new InputMismatchException();
	    		}
	    		res *= 10;
	    		res += c - '0';
	    		c = read();
	    	} while (!isSpaceChar(c));
	    	return res * sgn;
	    }
	    
	    public double nextDouble() 
	    {
	        int c = read();
	        while (isSpaceChar(c))
	        {
	        	c = read();
	        }
	        int sgn = 1;
	        if (c == '-')
	        {
	            sgn = -1;
	            c = read();
	        }
	        double res = 0;
	        while (!isSpaceChar(c) && c != '.') 
	        {
	            if (c == 'e' || c == 'E')
	            {
	            	return res * Math.pow(10, nextInt());
	            }
	            if (c < '0' || c > '9')
	            {
	            	throw new InputMismatchException();
	            }
	            res *= 10;
	            res += c & 15;
	            c = read();
	        }
	        if (c == '.') 
	        {
	            c = read();
	            double m = 1;
	            while (!isSpaceChar(c)) 
	            {
	                if (c == 'e' || c == 'E')
	                {
	                	return res * Math.pow(10, nextInt());
	                }
	                if (c < '0' || c > '9')
	                {
	                	throw new InputMismatchException();
	                }
	                m /= 10;
	                res += (c & 15) * m;
	                c = read();
	            }
	        }
	        return res * sgn;
	    }
	    
	    public String next()
	    {
	        int c = read();
	        while (isSpaceChar(c))
	        {
	        	c = read();
	        }
	        StringBuilder res = new StringBuilder();
	        do 
	        {
	            res.appendCodePoint(c);
	            c = read();
	        } while (!isSpaceChar(c));
	        return res.toString();
	    }

	    private boolean isSpaceChar(int c) 
	    {
	        return ' ' == c || '\n' == c || '\r' == c || '\t' == c || -1 == c;
	    }
	}
}