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.Collections.Generic;
using System.Text;
using System.Numerics;

namespace SolutionCS
{
    class Program
    {
        class modMCalc
        {
            public const int M = 1000000007;       // 素数(int範囲)

            // 乗算結果 % Mを求める
            static public int Mul(int a, int b)
            {
                return (int)(Math.BigMul(a, b) % M);
            }

            // 冪乗(mod M)
            static public int Pow(int a, int m)
            {
                if (0 == m)
                {
                    return 1;
                }
                if (1 == m)
                {
                    return a;
                }

                int result = 1;
                int param = a;
                for (; m > 0; m >>= 1)
                {
                    if ((m & 0x01) == 1)
                    {
                        result = Mul(result, param);
                    }

                    param = Mul(param, param);
                }

                return result;
            }

            // 除算(mod M)
            static public int Div(int a, int b)
            {
                return Mul(a, Pow(b, M - 2));
            }
        }

        class CombinationPermutation
        {
            private readonly int[] fac;

            // コンストラクタ
            // (mod Mの)階乗テーブル作成する
            public CombinationPermutation(int n)
            {
                fac = new int[n + 1];
                fac[0] = 1;
                for (int i = 1; i <= n; ++i)
                {
                    fac[i] = modMCalc.Mul(fac[i - 1], i);
                }
            }

            // 階乗求める
            public int Factorial(int n)
            {
                return fac[n];
            }

            // nCr
            public int nCr(int n, int r)
            {
                if (n < r) { return 0; }
                if (n == r) { return 1; }
                int res = Factorial(n);
                res = modMCalc.Div(res, Factorial(r));
                res = modMCalc.Div(res, Factorial(n - r));
                return res;
            }
        }

        static void Main(string[] args)
        {
            string[] inS = Console.ReadLine().Split(' ');
            int N = int.Parse(inS[0]);
            int M = int.Parse(inS[1]);

            int[] b = new int[M+2];

            b[0] = 0;
            for (int i = 0; i < M; i++)
            {
                b[i+1] = int.Parse(Console.ReadLine());

                // 一番最初以外が連続していたら終了
                if ( i != 0 && (b[i] + 1 == b[i+1]) )
                {
                    Console.WriteLine(0);
                    return;
                }
            }
            b[M+1] = N;

            CombinationPermutation c = new CombinationPermutation(N);

            int ans = 1;

            for (int i = 0; i <= M; i++)
            {
                int p = 0;
                int w = b[i + 1] - b[i] - 1;

                int s = w % 2;

                while(s <= w)
                {
                    int a = c.nCr(w, s);
                    p += a;
                    p %= modMCalc.M;
                    s += 2;
                }

                ans = modMCalc.Mul(ans, p);
            }


            Console.WriteLine(ans);
        }
    }
}