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 <bits/stdc++.h>

#define rev(v) reverse(v.begin(), v.end());
#define mx(v) max_element(v.begin(), v.end());
#define mn(v) min_element(v.begin(), v.end()); 
#define fastio() ios_base::sync_with_stdio(0);cout.tie(0);cin.tie(0);srand(time(NULL));
#define mod 1000000007

//ffs = lsb, clz = l0's, ctz = r0's, popcount = 1's 
 //++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++
using namespace std;
 //++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

int main(){
    fastio();
    int n,m ; cin >> n >> m;
    int dp[n + 1];
    for(int i = 0 ; i < n ;++i){
        dp[i] = 0;
    }
    dp[0] = 1;
    dp[1] = 1;
    for(int i = 0; i < m ; ++i){
        int x;  cin >> x;
        dp[x] = -1;
    } 
    
    for(int i = 2 ; i <= n ; ++i){
        if(dp[i] >= 0){
            if(dp[i-1] < 0  && dp[i-2] < 0 ){
                return cout << "0\n" , 0;
            }
            if(dp[i-1] < 0){
                dp[i] = dp[i - 2] % mod;
            }else if(dp[i-2] < 0){
                dp[i] = dp[i-1];
            }else{
                dp[i] = dp[i - 1] + dp[i - 2];
            }
            dp[i] = dp[i] % mod;
        }
    }

    return cout << dp[n] % mod, 0 ;
}