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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp86 {
    class Program {
        static void Main(string[] args) {
            var st = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = st[0];
            int M = st[1];
            int mod = 1000000007;

            var a = new int[M + 3];
            a[0] = -1;
            a[1] = 0;
            a[2] = 0;
            for (int i = 1; i <= M; i++) {
                a[i] = int.Parse(Console.ReadLine());
            }
            a[M + 1] = N + 1;

            var X = new int[N + 1];
            X[0] = 1;
            X[1] = 1;
            for (int i = 2; i <= N; i++) {
                X[i] = (X[i - 2] % mod + X[i - 1] % mod) % mod;
            }

            //Console.WriteLine("Xの配列は" + string.Join(" ", X));
            //Console.WriteLine("aの配列は" + string.Join(" ", a));

            long ans = 1;

            if (M == 0) {
                Console.WriteLine(X[N]);
                return;
            }

            if (N == 1) {
                Console.WriteLine(1);
                return;
            }
            if (N == 2) {
                if (M == 0) {
                    Console.WriteLine(2);
                    return;
                } else if (M == 1) {
                    Console.WriteLine(1);
                    return;
                } else {

                }
            }

            for (int i = 1; i <= M + 1; i++) {
                //Console.WriteLine("X[" + (a[i] - a[i - 1] - 1) + "] = " + X[a[i] - a[i - 1] - 1] + "を掛けました");

                if (a[i] - a[i - 1] >= 2) {
                    ans *= X[a[i] - a[i - 1] - 2];
                    ans %= mod;
                }

                if (a[i] - a[i - 1] == 1) {
                    ans *= 0;
                    Console.WriteLine(0);
                    return;
                }
            }

            Console.WriteLine(ans);
        }
    }
}