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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for (decay_t <decltype (n)> i = 0, i ## __len = (n); i < i ## __len; ++ i)

constexpr auto MOD = static_cast <int64_t> (1e+9+7);

auto main () -> int
{
  cin.tie (nullptr);
  ios::sync_with_stdio (false);

  size_t n, m;
  cin >> n >> m;

  vector <int> a (n + 1, 0);

  rep (i, m)
  {
    size_t a_;
    cin >> a_;
    a [a_] = 1;
  }
  vector <int64_t> ans (n + 1, 0);

  ans [0] = 1;
  rep (i, n)
  {
    if (a [i + 1] != 1)
    {
      ans [i + 1] += ans [i];
      ans [i + 1] %= MOD;
    }

    if (a [i + 2] != 1)
    {
      ans [i + 2] += ans [i];
      ans [i + 2] %= MOD;
    }
  }

  cout << ans [n] << endl;
}