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.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        final Scanner sc = new Scanner(System.in);

        final int N = sc.nextInt();
        final int M = sc.nextInt();

        boolean[] ok = new boolean[N+1];
        for (int i = 0; i <= N; i++) {
            ok[i] = true;
        }

        for (int i = 0; i < M; i++) {
            ok[sc.nextInt()] = false;
        }

        final int[] dp = new int[N+1];
        for (int i = 0; i <= N; i++) dp[i] = 0;

        dp[0] = 1;
        for (int i = 0; i < N; i++) {
            for (int j = i+1; j <= Math.min(N, i+2); j++) {
                if (ok[j]) {
                    dp[j] += dp[i];
                    dp[j] %= 1000000007;
                }
            }
        }

        System.out.println(dp[dp.length-1]);
    }
}