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.util.*;
import java.io.*;
import java.math.*;
public class A{
    class Node implements  Comparable<Node>{
        int id;
        long x;
        public Node(int id,long x){
            this.id=id; this.x=x;
        }
        public int compareTo(Node c){
            return Long.compare(this.x,c.x);
        }
    }

    void solve(){
        int n=ni(); int m=ni();
        int a[]=new int[m+1];
        long ans=1;
        for(int i=1;i<=m;i++) a[i]=ni();
        Arrays.sort(a,1,m+1);
        long pow[]=new long[1001];
        pow[0]=1;
        for(int i=1;i<=1000;i++) pow[i]=(pow[i-1]*2)%M;
        int totalzeros=n-m;
        long fact[]=new long[1001];
        fact[0]=1;
        for(int i=1;i<=1000;i++) fact[i]=(fact[i-1]*i)%M;
        ans=(ans*fact[totalzeros])%M;
       // for(int i=1;i<=m;i++) pw.print(a[i]+" ");
        for(int i=2;i<=m;i++){
            int d=a[i]-a[i-1]-1;

            if(d>0) {
                ans = (ans * pow[d - 1]) % M;
                ans = (ans * modInverse(fact[d], M)) % M;
            }

        }
        int d1=a[1]-1,d2=n-a[m];
        ans=(ans*modInverse(fact[d1],M))%M;
        ans=(ans*modInverse(fact[d2],M))%M;

        pw.println(ans);

    }
     long d, x, y;
     void extendedEuclid(long A, long B) {
        if(B == 0) {
            d = A;
            x = 1;
            y = 0;
        }
        else {
            extendedEuclid(B, A%B);
            long temp = x;
            x = y;
            y = temp - (A/B)*y;
        }
    }
     long modInverse(long A, long M)
    {
        extendedEuclid(A,M);
        return (x%M+M)%M;
    }

    static long M=(long)1e9+7;

    InputStream is;
    PrintWriter pw;
    String INPUT = "";
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        pw.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }

    public static void main(String[] args) throws Exception { new A().run(); }

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }

        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }


    private void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
}