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: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define print(s) cout << s << endl
#define acc(v) accumulate(v.begin(), v.end(), 0)
#define cinv(n,v) rep(i,n) cin >> v[i]
using namespace std;
const int INF = 1e9;
typedef long long ll;
typedef vector<int> vint;
typedef vector<string> vstr;
typedef vector<char> vchar;
const ll LINF = 1e18;
const ll MOD = 1e9 + 7;
// const lint MOD = 998244353;
int x_pos[4] = {1,0,-1,0}, y_pos[4] = {0,1,0,-1};
int ctoi(char c) {
	if (c >= '0' && c <= '9') {
		return c - '0';
	}
	return 0;
}
char upper(char c){
	return c-0x20;
}
char lower(char c){
	return c+0x20;
}

int gcd(int x, int y) {
  if (y == 0) return x;
  return gcd(y, x%y);
}

int main (){
	int n,m; cin >> n >> m;
	vector<int> a(m);
	cinv(m,a);
	vector<int> b(n+1);
	rep(i,m){
		b[a[i]] = 1;
	}
	vector<int> dp(n+1);
	dp[0]=1;
	for(int i = 1; i < n+1; i++){
		if (i==1){
			if (b[i]){
				dp[i]=0;
			}else{
				dp[i]=1;
			}
			continue;
		}
		if (b[i]){
			dp[i]=0;
			continue;
		}
		dp[i] = (dp[i-1] + dp[i-2])%MOD;
	}
	cout << dp[n] << endl;
}