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 static AtCoderer.Exter;
using static System.Math;
using System.Linq;

namespace AtCoderer
{

    public class App
    {
        public static void Solve()
        {
            int ind = 0;
            int[] r = readarr;
            int n = r[0];
            int m = r[1];
            int[] a = new int[m];
            for (int i = 0; i < m; i++)
                a[i] = readarr[0];
            long[] dp = new long[n+2];
            dp[0] = 0;
            dp[1] = 1;
            for (int i = 2; i < n + 2; i++)
            {
                if (ind >= m)
                    dp[i] = (dp[i - 1] + dp[i - 2]) % 1000000007;
                else
                {
                    if (a[ind] == i - 1)
                    {
                        dp[i] = 0;
                        ind++;
                    }
                    else
                    {
                        dp[i] = (dp[i - 1] + dp[i - 2]) % 1000000007;
                    }
                }
            }
            Console.WriteLine(dp[n+1]);
        }
        public static void Main(string[] args)
        {
            Solve();
            Console.ReadKey();
        }
    }
    public static class Exter
    {
        public static void rep(int loop, Action<int> act)
        {
            for (int i = 0; i < loop; i++)
                act(i);
        }
        public static int Max(params int[] p) => p.Max();
        public static long Max(params long[] p) => p.Max();
        public static int Min(params int[] p) => p.Min();
        public static long Min(params long[] p) => p.Min();
        public static int Gcd(int a, int b) => a > b ? GcdRecursive(a, b) : GcdRecursive(b, a);
        private static int GcdRecursive(int a, int b) => b == 0 ? a : GcdRecursive(b, a % b);
        public static void EnumArr<t>(this IEnumerable<t> v)
        {
            Console.WriteLine(string.Join(",", v));
        }
        public static string ToString(this IEnumerable<char> v)
        {
            return string.Join(",", v);
        }
        public static int[] readarr
        {
            get
            {
                return Console.ReadLine().Split().Select(s => int.Parse(s)).ToArray();
            }
        }
        public class UnionFind
        {
            private int[] Parent;
            private int GetRoot(int v)
            {
                if (Parent[v] < 0)
                    return v;
                else
                    return Parent[v] = GetRoot(Parent[v]);
            }
            public UnionFind(int size)
            {
                Parent = new int[size];
                for (int i = 0; i < size; i++)
                    Parent[i] = -1;
            }
            public bool AreGrouped(int a, int b)
            {
                return GetRoot(a) == GetRoot(b);
            }
            public void Connect(int a, int b)
            {
                a = GetRoot(a);
                b = GetRoot(b);
                if (a == b) return;
                if(Parent[b]<Parent[a])
                {
                    Parent[b] += Parent[a];
                    Parent[a] = b;
                }
                else
                {
                    Parent[a] += Parent[b];
                    Parent[b] = a;
                }
            }
            public int GetGroupSize(int a)
            {
                return -Parent[GetRoot(a)];
            }
        }
    }
}