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 PI 3.14159265359
#define rep(i,a,n) for(int i=a;i<(int)n;++i)
#define SZ(x) ((int)(x).size())	//size() unsigned -> int
#define descSort(a) sort(a.begin(),a.end(),std::greater<int>())
using namespace std;
typedef long long ll;
const ll INF = 1e9 + 7;
ll gcd(ll x,ll y){
    if(x%y==0)return y;
    return gcd(y,x%y);
}

int main(void){
    int n,m;
    cin>>n>>m;
    vector<ll> dp(n+1);
    rep(i,0,m){
        int a;
        cin>>a;
        dp[a]=-1;
    }
    if(dp[1]==-1){dp[1]=0;dp[2]=1;}
    else if(dp[2]==-1){dp[1]=1;dp[2]=0;}
    else {dp[1]=1;dp[2]=2;}
    rep(i,3,n+1){
        if(dp[i]==-1)dp[i]=0;
        else dp[i]=(dp[i-1]+dp[i-2])%INF;
    }
    cout<<dp[n]<<endl;
    return 0;
}