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: Wrong Answer)

using System;
using System.Linq;

namespace abc129
{
    class C
    {
        static public long[] memo;

        static void Main(string[] args)
        {
            const int MOD = 1000000007;

            var input = Input.IntArray();
            var N = input[0];
            var M = input[1];

            C.memo = new long[N + 1];
            C.memo[0] = 1;
            C.memo[1] = 1;

            long res = 1;

            int now = 0;
            for (int i = 0; i < M; i++)
            {
                int holl = Input.Int();
                // 着地後も穴
                if (holl == now) {
                    Console.WriteLine(0);
                    return;
                }

                res = (res * C.getPattern(holl - now - 1)) % MOD;
                now = holl + 1;
            }

            res = (res * C.getPattern(N - now)) % MOD;

            Console.WriteLine(res);

        }

        static long getPattern(long num)
        {
            if (num < 2) {
                return 1;
            }
            if (C.memo[num] == 0) {
                C.memo[num] = C.getPattern(num - 1) + C.getPattern(num - 2);
            }
            return C.memo[num];
        }

        /** Input Class */
        internal static class Input
        {
            /** input int */
            public static int Int() => int.Parse(Console.ReadLine());

            /** input str */
            public static string Str() => Console.ReadLine();

            /** input array of int */
            public static int[] IntArray() => Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

            /** input array of string */
            public static string[] StrArray() => Input.Str().Split(' ');

            /** input array of char */
            public static char[] charArray() => Input.Str().ToCharArray();
        }

    }
}