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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#define lout cout
#else
stringstream devnull;
#define lout devnull
#endif
template <class C>
inline void vcin(C &a);
template <class C>
inline void vcout(const C a, const string separate = "\n");

int main()
{
  const int P = 1000000007;
  int n, m;
  cin >> n >> m;
  vector<int> a(m);
  vcin(a);

  vector<int> c(n + 1 + 2, -1);
  for (int i = 0; i < m; i++)
  {
    c[a[i] + 2] = 0;
  }
  c[-1 + 2] = 0;
  c[0 + 2] = 1;
  for (int i = 1 + 2; i <= n + 2; i++)
    if (c[i] != 0)
    {
      c[i] = (c[i - 1] % P + c[i - 2] % P) % P;
    }

#ifdef LOCAL
  vcout(c);
  cout << endl;
#endif
  cout << c[n + 2] << endl;

  return 0;
}

template <class C>
inline void vcin(C &c)
{
  for (auto &a : c)
  {
    cin >> a;
  }
}
template <class C>
inline void vcout(const C c, const string separate)
{
  for (auto it = c.begin(); it != c.end(); it++)
  {
    if (it != c.begin())
      cout << separate;
    cout << *it;
  }
}