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.*;

class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int stepNum = sc.nextInt();
		int brokenNum = sc.nextInt();
		int[] brokenSteps = new int[brokenNum];
		for(int i = 0; i < brokenNum; i++)brokenSteps[i] = sc.nextInt();
        
        Dp dp = new Dp(stepNum+1);
        for(int index : brokenSteps) Dp.dp[index] = 0;
        int ans = dp.part(stepNum);

		System.out.println(ans);
    }
}

class Dp {
    public static int[] dp;
    public Dp (int num) {
        dp = new int[num];
        for(int i = 0; i < num; i++)dp[i] = -1;
    }

    public int part(int index) {
        if(dp[index] != -1)return dp[index];
        if(index == 0) dp[index] = 1;
        else if(index == 1) dp[index] = 1;
        else dp[index] = part(index-1) + part(index-2);
        while(dp[index] >= Mod.mod) dp[index] -= Mod.mod;
        return dp[index];
    }
}

class Mod{
    static int mod = 1000000007;
}