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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;

public class Main {

    public static void main(String[] args) throws Exception {
        try (Reader r = new Reader(System.in)) {
            int N = r.i();
            int M = r.i();

            boolean[] A = new boolean[N + 1];
            for (int i = 1; i <= M; i++) {
                int a = r.i();
                A[a] = true;
            }

            long[] dp = new long[N + 1];
            dp[0] = 1;

            for (int i = 1; i <= N; i++) {
                if (A[i]) {
                    continue;
                }

                if (i == 1) {
                    dp[1] = dp[0];
                } else {
                    dp[i] = (dp[i - 1] + dp[i - 2]) % 1000000007;
                }
            }

            System.out.println(dp[N]);
        }
    }

    public static class Reader implements AutoCloseable {

        private BufferedReader br;

        private String[] buf;

        private int bufidx = -1;

        public Reader(InputStream in) {
            this.br = new BufferedReader(new InputStreamReader(in));
        }

        @Override
        public void close() throws Exception {
            br.close();
        }

        private void readBuf() throws IOException {
            if (bufidx == -1 || bufidx == buf.length) {
                buf = br.readLine().split(" ");
                bufidx = 0;
            }
        }

        public String s() throws IOException {
            readBuf();
            return buf[bufidx++];
        }

        public int i() throws IOException {
            return Integer.parseInt(s());
        }

        public long l() throws IOException {
            return Long.parseLong(s());
        }

        public double d() throws IOException {
            return Double.parseDouble(s());
        }

        public String[] sa() throws IOException {
            readBuf();
            if (bufidx != 0) {
                throw new RuntimeException("illegal read");
            }
            bufidx = -1;
            return buf;
        }

        public int[] ia() throws IOException {
            String[] sa = sa();
            int[] ia = new int[sa.length];
            for (int i = 0; i < sa.length; i++) {
                ia[i] = Integer.parseInt(sa[i]);
            }
            return ia;
        }

        public long[] la() throws IOException {
            String[] sa = sa();
            long[] la = new long[sa.length];
            for (int i = 0; i < sa.length; i++) {
                la[i] = Long.parseLong(sa[i]);
            }
            return la;
        }

        public double[] da() throws IOException {
            String[] sa = sa();
            double[] da = new double[sa.length];
            for (int i = 0; i < sa.length; i++) {
                da[i] = Double.parseDouble(sa[i]);
            }
            return da;
        }

        public int[][] im(int N) throws IOException {
            int[][] im = new int[N][];
            for (int i = 0; i < N; i++) {
                im[i] = ia();
            }
            return im;
        }

        public long[][] lm(int N) throws IOException {
            long[][] lm = new long[N][];
            for (int i = 0; i < N; i++) {
                lm[i] = la();
            }
            return lm;
        }

        public double[][] dm(int N) throws IOException {
            double[][] dm = new double[N][];
            for (int i = 0; i < N; i++) {
                dm[i] = da();
            }
            return dm;
        }

    }

}