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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

class Program {
    static void Main() {
        int[] input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        int n = input[0], m = input[1];
        int[] a = new int[m], b = new int[m + 1];
        for(int i = 0; i < m; i++) a[i] = int.Parse(Console.ReadLine());
        b[0] = a[0];
        for(int i = 1; i < m; i++) b[i] = a[i] - a[i - 1] - 1;
        b[m] = n - a[m - 1];
        ModInt pro = 1;
        for(int i = 0; i < m + 1; i++) pro *= ModInt.Fib(b[i]);
        Console.WriteLine((int) pro);
    }
}

struct ModInt {
    const int MOD = 1000000007;
    long value;
    
    static List<ModInt> fib = new List<ModInt> { 0, 1 };

    public ModInt(long value) { this.value = value; }
    public static implicit operator ModInt(long a) => new ModInt(a % MOD + (a < 0 ? MOD : 0));
    public static explicit operator int(ModInt a) => (int) a.value;
    public static ModInt operator +(ModInt a, ModInt b) => a.value + b.value;
    public static ModInt operator *(ModInt a, ModInt b) => a.value * b.value;
    public static ModInt Fib(int n) {
        for(int i = fib.Count(); i <= n; i++) fib.Add(fib[i - 2] + fib[i - 1]);
        return fib[n];
    }
}