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;

namespace CTypicalStairs
{
    class Program
    {
        const int LAW = 1000000007;

        static void Main(string[] args)
        {
            // 入力の取得
            var inputs = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var n = inputs[0];
            var m = inputs[1];

            // 壊れている床の一覧を取得
            var brokenStairs = new int[m];
            for (var i = 0; i < m; i++)
            {
                brokenStairs[i] = int.Parse(Console.ReadLine());
            }

            // 連続する壊れていない床の距離を計算
            var distances = new int[m + 1];
            for (var i = 0; i <= m; i++)
            {
                var current = i != m ? brokenStairs[i] : n + 1;
                var prev = i != 0 ? brokenStairs[i - 1] : -1;

                // 壊れた階段が連続していたら、0を出力して終了
                if (current - prev == 1)
                {
                    Console.WriteLine(0);
                    return;
                }

                distances[i] = (current - 1) - (prev + 1);
            }

            // 0 ~ a1 - 1 まで P1 通り、a1 + 1 ~ a2 - 1 まで P2 通り… am + 1 ~ N まで Pm+1 通り
            // 総数は P1 * P2 * … * Pm+1 通り
            var maxDistance = distances.Max();
            var patternMap = CalcPatternMap(Math.Max(maxDistance, 1));

            var patternCount = 1;
            foreach (var distance in distances)
            {
                patternCount = (int)(Math.BigMul(patternCount, patternMap[distance]) % LAW);
            }

            // 解答の出力
            Console.WriteLine(patternCount);
        }

        /// <summary>
        /// 各距離までの経路数 % 1000000007 の一覧を返す
        /// </summary>
        /// <param name="maxDistance"></param>
        /// <returns></returns>
        static int[] CalcPatternMap(int maxDistance)
        {
            var patternMap = new int[maxDistance + 1];

            patternMap[0] = 1;
            patternMap[1] = 1;
            for (var i = 2; i <= maxDistance; i++)
            {
                patternMap[i] = (patternMap[i - 2] + patternMap[i - 1]) % LAW;
            }

            return patternMap;
        }
    }
}