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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int number_n, number_m, i, j = 0;
    number_n = Integer.parseInt(sc.next());
    number_m = Integer.parseInt(sc.next());
    int[] stage = new int[number_n+1];
    int[] broken_stage = new int[number_m+1];
    broken_stage[0] = 0;
    for(i = 0; i < number_m; i++) {
      broken_stage[i] = Integer.parseInt(sc.next());
    }
    stage[0] = 1;
    stage[1] = (broken_stage[0] == 1)? 0 : 1;
    for(i = 2; i <= number_n; i++) {
      stage[i] = (stage[i-1] + stage[i-2]);
      for(; j < number_m; j++) {
        if(broken_stage[j] < i) {
          continue;
        } else if(broken_stage[j] > i) {
          break;
        } else {
          stage[i] = 0;
          break;
        }
      }
      if(stage[i] > 1000000007) stage[i] -= 1000000007;
    }
    System.out.println(stage[number_n]);
  }
}