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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TypicalStairs solver = new TypicalStairs();
        solver.solve(1, in, out);
        out.close();
    }

    static class TypicalStairs {
        public static int MOD = 1_000_000_007;

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();

            int[] stairs = new int[n + 1];
            long[] route = new long[n + 1];

            for (int i = 1; i <= m; i++) {
                int step = in.nextInt();
                stairs[step] = 1;
                if (stairs[step - 1] == 1) {
                    out.print(0);
                    return;
                }
            }

            route[0] = 1;
            if (stairs[1] == 0) {
                route[1] = 1;
            }

            if (n <= 1) {
                out.print(route[1]);
                return;
            }

            if (stairs[2] == 0) {
                route[2] = 1;
            }
            for (int i = 1; i <= n - 1; i++) {
                if (stairs[i] == 1) {
                    continue;
                }
                if ((i + 1) <= n && stairs[i + 1] == 0) {
                    route[i + 1] = (route[i] + route[i + 1]) % MOD;
                }
                if ((i + 2) <= n && stairs[i + 2] == 0) {
                    route[i + 2] = (route[i] + route[i + 2]) % MOD;
                }
            }

            out.print(route[n] % MOD);

        }

    }
}