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: Wrong Answer)

#include <iostream>
#include<vector>
#include<queue>
#include<algorithm>
#include<string>
#include <string.h>

#define REP(i,n) for(int i=0;i<n;i++)

using namespace std;

long mem[100000];

long fib(long i) {
    if(mem[i] != -1) return mem[i];
    if(i==0 || i == 1) return 1;
    return mem[i] = fib(i-1) + fib(i-2);
}

int main() {
    long n,m;
    cin >>n>>m;
    vector<long> v(m+2);
    long res =1;
    int flag = 0;
    v[0] = 0;
    memset(mem, -1, sizeof(mem));
    for(long i=0; i<m;i++){
        cin >> v[i+1];
        if(v[i+1] != 1) {
            if(v[i+1] -v[i]== 1) {
                flag =1;
                break;
            }
        }

        if(i == 0) res *= fib(v[i+1]-1);
        else res *= fib(v[i+1]-1 - v[i]-1);
    }

    if(flag == 1) cout << 0 << endl;
    else cout << (res*fib(n-v[m]-1))%1000000007 <<endl;
}