Problem:
Score : 300 points

Problem Statement

There is a staircase with N steps. Takahashi is now standing at the foot of the stairs, that is, on the 0-th step.
He can climb up one or two steps at a time.

However, the treads of the a_1-th, a_2-th, a_3-th, \ldots, a_M-th steps are broken, so it is dangerous to set foot on those steps.

How many are there to climb up to the top step, that is, the N-th step, without setting foot on the broken steps?
Find the count modulo 1\ 000\ 000\ 007.

Constraints

1 \leq N \leq 10^5

0 \leq M \leq N-1

1 \leq a_1 < a_2 < ... < a_M \leq N-1

Input

Input is given from Standard Input in the following format:

N M
a_1
a_2
.
.
.
a_M

Output

Print the number of ways to climb up the stairs under the condition, modulo 1\ 000\ 000\ 007.

Sample Input 1

6 1
3

Sample Output 1

4

There are four ways to climb up the stairs, as follows:

0 \to 1 \to 2 \to 4 \to 5 \to 6

0 \to 1 \to 2 \to 4 \to 6

0 \to 2 \to 4 \to 5 \to 6

0 \to 2 \to 4 \to 6

Sample Input 2

10 2
4
5

Sample Output 2

0

There may be no way to climb up the stairs without setting foot on the broken steps.

Sample Input 3

100 5
1
23
45
67
89

Sample Output 3

608200469

Be sure to print the count modulo 1\ 000\ 000\ 007.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;

public class Main
{
  final int mod = (int)1e9+7;
  int n, m;
  boolean[] a;
  int[] dp;
  
  Main(Scanner in, PrintWriter out)
  {
	n = in.nextInt();
    m = in.nextInt();
    a = new boolean[n+2];
    for (int i = 0; i < m; i++)
      a[in.nextInt()] = true;
    dp = new int[n];
    Arrays.fill(dp, -1);
    out.println(dp(0));
  }
  
  int dp(int at)
  {
    if (at == n) return 1;
    if (at > n) return 0;
    if (dp[at] != -1) return dp[at];
    int cnt = 0;
    if (!a[at+1]) cnt += dp(at+1);
    cnt %= mod;
    if (!a[at+2]) cnt += dp(at+2);
    cnt %= mod;
    return dp[at] = cnt % mod;
  }

  public static void main(String[] args)
  {
    Scanner in = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
    new	Main(in, out);
    out.close();
  } 
}