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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using P = pair<ll, ll>;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define M 1000000007

ll powll(ll x, ll y) {
    ll re=1;
    rep(i, y) {
        re = re * x % M;
    }
    return re;
}


int main() {

    int n,m;
    cin >> n>>m;

    vector<ll> step(100001, 0);
    vector<bool> bstep(100001, true);

    rep(i, m) {
        int x;
        cin >> x;
        bstep[x] = false;
    }

    step[0] = 1;
    if (bstep[1] == true) {
        step[1] = 1;
    }

    for (int i = 2; i <= n; i++) {
        if (bstep[i] == true) {
            step[i] += step[i - 1] % M;
            step[i] += step[i - 2] % M;
        }
    }
    cout << step[n];

    return 0;
}