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.Linq;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using static System.Console;
using static Program.Input;
using static Program.MyMath;
using static Program.Const;

namespace Program
{
    static class Const
    {
        public static string alp = "abcdefghijklmnopqrstuvwxyz";
        public static string Alp = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
        public const long MOD = 1000000007;
        public static int INF = int.MaxValue;
        public static long INFL = long.MaxValue;
    }
    public class Program
    {
        public static void Main()
        {
          int n,m; InputLine(out n, out m);
          var a = new bool[n+1];
          
          for(int i=0; i<m; i++) a[ScanInt()] = true;
          var dp = new long[n+1];
          dp[0] = 1;
          dp[1] = a[1] ? 0 : 1;
          for(int i=2; i<=n; i++){
            if(a[i]) continue;
            if(!a[i-1]) dp[i] = dp[i-1];
            if(!a[i-2]) dp[i] = (dp[i] + dp[i-2]) % MOD;
          }
          WriteLine(dp[n]);
        }
    }
    static class Input
    {
        public static void InputLine(out int a, out int b) { var input = ScanIntArray(); a = input[0]; b = input[1]; }
        public static void InputLine(out int a, out int b, out int c) { var input = ScanIntArray(); a = input[0]; b = input[1]; c = input[2]; }
        public static void InputLine(out int a, out int b, out int c, out int d) { var input = ScanIntArray(); a = input[0]; b = input[1]; c = input[2]; d = input[3]; }

        public static void InputLine(out long a, out long b) { var input = ScanLongArray(); a = input[0]; b = input[1]; }
        public static void InputLine(out long a, out long b, out long c) { var input = ScanLongArray(); a = input[0]; b = input[1]; c = input[2]; }
        public static void InputLine(out long a, out long b, out long c, out long d) { var input = ScanLongArray(); a = input[0]; b = input[1]; c = input[2]; d = input[3]; }

        public static void InputLine(out string a, out string b) { var input = ScanStrArray(); a = input[0]; b = input[1]; }

        public static int ScanInt() { return int.Parse(ReadLine()); }
        static public uint ScanUint() { return uint.Parse(ReadLine()); }
        static public double ScanDouble() { return double.Parse(ReadLine()); }
        static public long ScanLong() { return long.Parse(ReadLine()); }
        static public ulong ScanUlong() { return ulong.Parse(ReadLine()); }
        static public int[] ScanIntArray() { return ReadLine().Split().Select(x => int.Parse(x)).ToArray(); }
        static public uint[] ScanUintArray() { return ReadLine().Split().Select(x => uint.Parse(x)).ToArray(); }
        static public double[] ScanDoubleArray() { return ReadLine().Split().Select(x => double.Parse(x)).ToArray(); }
        static public long[] ScanLongArray() { return ReadLine().Split().Select(x => long.Parse(x)).ToArray(); }
        static public ulong[] ScanUlongArray() { return ReadLine().Split().Select(x => ulong.Parse(x)).ToArray(); }

        static public string ScanStr() { return ReadLine(); }
        static public string[] ScanStrArray() { return ScanStr().Split(); }
        static public string RegaxReplace(this string arg1, string pattern, string replacement) { return Regex.Replace(arg1, pattern, replacement); }
    }
    static class MyMath
    {
        static public int CountBit(this long a) { if (a == 0) return 0; int c = 1; for (; a > 1; a /= 2) if (a % 2 == 1) c++; return c; }
        static public int Floor2(this int a) { int N = 1; while (N < a) N *= 2; return N / 2; }
        static public long Floor2(this long a) { long N = 1; while (N < a) N *= 2; return N / 2; }
        static public int Ceiling2(this int a) { int N = 1; while (N < a) N *= 2; return N; }
        static public long Ceiling2(this long a) { long N = 1; while (N < a) N *= 2; return N; }
        static public long[] CumSum(this long[] a) { var res = new long[a.Length]; long s = 0; for (int i = 0; i < a.Length; i++) res[i] = (s += a[i]); return res; }
        static public IEnumerable<int> PrimeFactors(this int n)
        {
            int tmp = n;
            for (int i = 2; i * i <= n; i++) while (tmp % i == 0) { tmp /= i; yield return i; }
            if (tmp != 1) yield return tmp;
        }
        static public IEnumerable<long> PrimeFactors(this long n)
        {
            var tmp = n;
            for (long i = 2; i * i <= n; i++) while (tmp % i == 0) { tmp /= i; yield return i; }
            if (tmp != 1) yield return tmp;
        }
        static public int Digit(this int n, int d) { if (d < 0) return 0; return (n % (int)Math.Pow(10, d + 1)) / (int)Math.Pow(10, d); }
        static public int Length(this int n) { if (n < 0) return 0; return (int)Math.Log10(n) + 1; }
        static public int Top(this int n) { return n.Digit(n.Length() - 1); }
        public static bool isPrime(this int p)
        {
            if (p <= 1) return false;
            for (int i = 2; i * i <= p; i++) if (p % i == 0) return false;
            return true;
        }
        public static bool isPrime(this long p)
        {
            if (p <= 1) return false;
            for (long i = 2; i * i <= p; i++) if (p % i == 0) return false;
            return true;
        }
        public static int GCD(int a, int b)
        {
            Func<int, int, int> gcd = null;
            gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
            return a > b ? gcd(a, b) : gcd(b, a);
        }
        public static long GCD(long a, long b)
        {
            Func<long, long, long> gcd = null;
            gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
            return a > b ? gcd(a, b) : gcd(b, a);
        }
        public static ulong extGCD(ulong a, ulong b, ref ulong x, ref ulong y)
        {
            if (b == 0) { x = 1; y = 0; return a; }
            var d = extGCD(b, a % b, ref y, ref x);
            y -= a / b * x;
            return d;
        }
        public static int LCM(int a, int b) { return a * b / GCD(a, b); }
        public static long LCM(long a, long b) { return a * b / GCD(a, b); }
        public static long Inv(this long a, long m = MOD)
        {
            long b = m, u = 1, v = 0;
            while (b != 0)
            {
                long t = a / b;
                a -= t * b;
                swap(ref a, ref b);
                u -= t * v;
                swap(ref u, ref v);
            }
            u %= m;
            if (u < 0) u += m;
            return u;
        }
        private static void swap(ref long a, ref long b) { var t = a; a = b; b = t; }
        public static long ModPow(long a, long n, long m = MOD)
        {
            long res = 1;
            while (n > 0)
            {
                if (n % 2 == 1) res = (res * a) % m;
                a = (a * a) % m;
                n >>= 1;
            }
            return res;
        }
    }

    static class MyLinq
    {
        public static void Sort(this string[] array) { Array.Sort(array, StringComparer.OrdinalIgnoreCase); }
        public static void StringSort(this List<string> list) { list.Sort(StringComparer.OrdinalIgnoreCase); }
        public static string Join<T>(this IEnumerable<T> source, string separator) { return string.Join(separator, source); }
        public static IEnumerable<TItem> Distinct<TItem, TKey>(this IEnumerable<TItem> source, Func<TItem, TKey> keySelector)
        {
            if (source == null)
                throw new ArgumentNullException(nameof(source));

            if (keySelector == null)
                throw new ArgumentNullException(nameof(keySelector));

            var set = new HashSet<TKey>();
            foreach (var item in source)
                if (set.Add(keySelector(item))) yield return item;
        }
    }
}