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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<iostream>
#include<algorithm>
#include<ctime>
#include<vector>
#include<string>
#include<cmath>
#include<map>
#include<iomanip>
#include<numeric>
#include<queue>
#include<deque>
#include<cfloat>
#include<functional>
#include<tuple>
#include<math.h>
#include<bitset>
#include<stack>
#include<set>
#include<random>
#include<stdlib.h>
#define rip(i,n) for(ll i=0;i<n;i++)
#define Rip(i,n) for(ll i=1;i<=n;i++)
#define all(V) V.begin(),V.end()
#define ll long long
#define ld long double
#define MOD 1000000007
#define mod 998244353
#define sec setprecision
#define Pair pair<ll,ll>
#define _CRT_SECURE_NO_WARNINGS
#pragma target("avx")
#pragma optimize("O3")
#pragma optimize("unroll-loops")
constexpr double eps = 1e-9;
constexpr double pi = 3.141592653589793238462643383279;
using namespace std;
ll gcd(ll a, ll b)
{
	if (a % b == 0)	return(b);
	else return(gcd(b, a % b));
}
ll lcm(ll a, ll b)
{
	return a * b / gcd(a, b);
}
ll pow(ll x, ll n) {
	x %= mod;
	if (n == 0)
		return 1;
	if (n % 2 == 0)
		return (pow((x * x) % mod, n / 2) % mod);
	else
		return (x * pow(x, n - 1)) % mod;
}
int main() {
	int n, m; cin >> n >> m;
	vector<int>a(m); rip(i, m)cin >> a[i];
	vector<int>dp(n+1,0);//dp[i]deidannmeniikutoori
	dp[0] = 1;
	rip(i, m)dp[a[i]] = 0;
	vector<bool>pd(n + 1, true);
	rip(i, m)pd[a[i]] = false;
	for (int i = 1; i <= n; i++) {
		if (pd[i] == true) {
			if (i == 1)dp[i] = 1;
			else dp[i] = (dp[i - 1]%MOD + dp[i - 2]%MOD);
		}
	}
	cout << dp[n]%MOD << endl;
}