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.math.BigInteger;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int M = Integer.parseInt(sc.next());
        int [] Ai = new int[M];
        int [] distanceArray = new int[M+1];

        for (int i = 0; i < M; i++) {

            Ai[i] = Integer.parseInt(sc.next());

            if (i == 0) {

                distanceArray[0] = Ai[0]-1;
            }  else {

                if (Ai[i] == Ai[i]-1) {

                    System.out.println(0);
                    System.exit(0);
                }

                distanceArray[i] = (Ai[i]-1) - (Ai[i-1] + 1);
            }

            if (distanceArray[i] < 0 ) {

                System.out.println(0);
                System.exit(0);
            }
        }

        sc.close();

        distanceArray[M] = N - (Ai[M-1]+1);

        if (distanceArray[M] < 0 ) {

            System.out.println(0);
            System.exit(0);
        }

        BigInteger ans = BigInteger.ONE;

        for (int i =0; i < M+1; i++) {

            ans = ans.multiply(fanc(distanceArray[i]));
        }

        System.out.println(ans.remainder(BigInteger.valueOf(1000000007)));
    }

    public static BigInteger fanc(int num) {

        if (num == 1) {

            return BigInteger.ONE;
        }
        if (num == 2) {

            return BigInteger.ONE.add(BigInteger.ONE);
        }
        return fanc(num - 1).add(fanc(num - 2));
    }

}