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.Scanner;

/**
 * @author yoshizaki
 * abc 129
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner= new Scanner(System.in);
        int step = scanner.nextInt();
        int ng = scanner.nextInt();
        long [] dp = new long[step];
        for(int i = 0; i < step; i++) dp[i] = 0;
        if (ng > 0) {
            int [] breaks = new int[step];
            for(int i = 0; i < ng ; i++) breaks[i] = scanner.nextInt();
            for(int i = 0; i < ng; i++) dp[breaks[i]-1] = -100000000000000000l;
        }
        
        if(step > 1) {
            if (dp[0] == 0 && dp[1] == 0) {
                dp[0] = 1;
                dp[1] = 2;
            } else if (dp[0] == 0) {
                dp[0] = 1;
            } else if (dp[1] == 0) {
                dp[1] = 1;
            }
            for(int i = 2; i < step; i++) {
                if (dp[i] < 0) continue;
                if (dp[i-1] > 0) dp[i] += dp[i-1];
                if (dp[i-2] > 0) dp[i] += dp[i-2];
                dp[i] %= 1000000007;
            }
        } else {
            dp[step - 1] = 1;
        }
        System.out.println(dp[step-1]);
    }
}