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.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.fill;
import static java.lang.Math.*;
import static java.util.Arrays.sort;
import static java.util.Collections.sort;


public class C294 
{

	public static int mod = 1000000007;
	public static long INF = (1L << 60);
	static FastScanner2 sc = new FastScanner2();
	static OutputWriter out = new OutputWriter(System.out);
	static long[][] nCr=new long[1001][1001];
	public static void precalculate()
	{
		nCr[0][0]=1;
		for(int i=1;i<=1000;i++)
		{
			nCr[i][0]=1;
		}
		for(int i=1;i<=1000;i++)
		{
			for(int j=1;j<=i;j++)
			{
				if(i==j)
				{
					nCr[i][j]=1;
					continue;
				}
				nCr[i][j]=(nCr[i-1][j]+nCr[i-1][j-1])%mod;
			}
		}
	}
	public static void main(String[] args) 
	{

		int[][] comb = new int[1001][1001];
		comb[0][0] = 1;
		for(int i = 1; i <= 1000; ++i)
		{
			comb[i][0] = 1;
			for(int j = 1; j <= i; ++j)
				comb[i][j] = (comb[i-1][j] + comb[i-1][j-1])%mod;
		}
		
		int n = sc.nextInt(), m = sc.nextInt();
		boolean[] on = new boolean[n];
		for(int i = 0; i < m; ++i)
			on[sc.nextInt() - 1] = true;
		
		long res = 1;
		int off = n - m, seg = 0;
		boolean onBefore = false;
		for(int i = 0; i < n; ++i)
			if(on[i])
			{
				if(seg > 0)
				{				 
					if(onBefore)
						res = (res * pow(seg - 1))%mod;
					res = (res * comb[off][seg])%mod;
					off -= seg;
					seg = 0;
				}
				onBefore = true;
			}
			else
				++seg;
		
		out.println(res);
		out.close();

	}
	static int pow(int exp)
	{
		int ret = 1;
		while(exp-- > 0)
			ret = (ret<<1)%mod;
		return ret;
	}
	
	public static long pow(long x, long n) 
	{
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p)) 
		{
			if ((n & 1) != 0) 
			{
				res = (res * p);
			}
		}
		return res;
	}
	
	public static long pow(long x, long n, long mod) 
	{
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) 
		{
			if ((n & 1) != 0) 
			{
				res = (res * p % mod);
			}
		}
		return res;
	}

	public static long gcd(long n1, long n2)
	{
		long r;
		while (n2 != 0) 
		{
			r = n1 % n2;
			n1 = n2;
			n2 = r;
		}
		return n1;
	}

	public static long lcm(long n1, long n2) 
	{
		long answer = (n1 * n2) / (gcd(n1, n2));
		return answer;
	}

	static class FastScanner2 
	{
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

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

		public String nextLine() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			return res.toString();
		}

		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 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 int[] nextIntArray(int n)
		{
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) 
			{
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n)
		{
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) 
			{
				arr[i] = nextLong();
			}
			return arr;
		}

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

		private boolean isEndOfLine(int c) 
		{
			return c == '\n' || c == '\r' || c == -1;
		}
	}

	static class InputReader 
	{
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputstream) 
		{
			reader = new BufferedReader(new InputStreamReader(inputstream));
			tokenizer = null;
		}

		public String nextLine() 
		{
			String fullLine = null;
			while (tokenizer == null || !tokenizer.hasMoreTokens())
			{
				try 
				{
					fullLine = reader.readLine();
				} catch (IOException e)
				{
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}

		public String next()
		{
			while (tokenizer == null || !tokenizer.hasMoreTokens()) 
			{
				try 
				{
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) 
				{
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public long nextLong() 
		{
			return Long.parseLong(next());
		}

		public int[] nextIntArray(int n) 
		{
			int a[] = new int[n];
			for (int i = 0; i < n; i++) 
			{
				a[i] = nextInt();
			}
			return a;
		}

		public long[] nextLongArray(int n)
		{
			long a[] = new long[n];
			for (int i = 0; i < n; i++) 
			{
				a[i] = nextLong();
			}
			return a;
		}

		public int nextInt() 
		{
			return Integer.parseInt(next());
		}
	}

	static class OutputWriter 
	{
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) 
		{
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer)
		{
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects)
		{
			for (int i = 0; i < objects.length; i++) 
			{
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void println(Object... objects)
		{
			print(objects);
			writer.println();
		}

		public void close() 
		{
			writer.close();
		}

		public void flush() 
		{
			writer.flush();
		}
	}

}