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: Runtime Error)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String[] str = br.readLine().split(" ");

		int N = Integer.parseInt(str[0]);
		int M = Integer.parseInt(str[1]);

		int[] a = new int[M];
		for(int i=0;i<M;i++) {
			a[i] = Integer.parseInt(br.readLine());
		}

		int pa = 0;



		int n = 0;
		int r = 0;

		long ans = 1;
		for(int i = 0;i<M;i++) {
			if(i ==0) {
				n = a[i]-1;
				r = 0;
				while(n>=r) {
					pa += calcNumOfCombination(n, r);

					n -= 1;
					r += 1;
				}

			}else {

				n = (a[i]-1)-(a[i-1]+1);
				r = 0;
				while(n>=r) {
					pa += calcNumOfCombination(n, r);

					n -= 1;
					r += 1;
				}

			}
			ans = ans * pa;
			pa = 0;
		}

		n = N-(a[M-1]+1);
		r = 0;
		while(n>=r) {
			pa += calcNumOfCombination(n, r);

			n -= 1;
			r += 1;
		}

		ans = ans * pa;

		ans = ans % 1000000007;


		int flg = 0;
		for(int i=0;i<M;i++) {
			if(i!=0) {
				if(a[i-1]==a[i]) {
					System.out.println(0);
					flg = 1;
				}
			}
		}

		if(flg == 0) {
			System.out.println(ans);
		}


	}


    static int calcNumOfCombination(int n, int r){
        int num = 1;
        for(int i = 1; i <= r; i++){
            num = num * (n - i + 1) / i;
        }
        return num;
    }
}