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;
typedef long long ll;
int main(void){
    ll MOD = 1000000007;
    int N, M;
    cin >> N >> M;
    
    vector<int> a(M);
    for (int i = 0; i < M; i++)
        cin >> a[i];
    
    vector<ll> dp(N+1, 0);
    dp[0] = 1;
    int a_idx = 0;
    if (a[a_idx] != 1)
        dp[1] = 1;
    else
        a_idx++;

    for (int i = 2; i < N+1; i++) {
        if (a_idx != M)
            if (a[a_idx] == i) {
                a_idx++;
                dp[i] = 0;
            }
            else
                dp[i] = (dp[i-1] + dp[i-2]) % MOD;
        else
            dp[i] = (dp[i-1] + dp[i-2]) % MOD;
    }
    cout << dp[N] << endl;
}