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 <bits/stdc++.h>

#define debug(x) cout <<"DEBUG"<<" "<< #x << ":" << x << '\n'
#define rep(i,n) for(int_fast32_t i = 0; i < ((int_fast32_t)(n)); i++)   // 0-indexed up
#define rep1(i,n) for(int_fast32_t i = 1; i <= ((int_fast32_t)(n)); i++) // 1-indexed up
#define rrep(i,n) for(int_fast32_t i = ((int_fast32_t)(n)-1); i >= 0; i--)  // 0-indexed down
#define rrep1(i,n) for(int_fast32_t i = ((int_fast32_t)(n)); i >= 1; i--)   // 1-indexed down
#define all(x) (x).begin(),(x).end()

using namespace std;

template<typename T>
using vec = vector<T>;
using i32 = int_fast32_t;
using i64 = int_fast64_t;
using u32 = uint_fast32_t;
using u64 = uint_fast64_t;
using ll = long long;
using ld = long double;
using vi = vec<int_fast32_t>;
using vl = vec<int_fast64_t>;
using vld = vec<ld>;
using vii = vec<vi>;
using PII = pair<int_fast32_t, int_fast32_t>;

template<class T>
using maxheap = std::priority_queue<T>;
template<class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;

template<class T,class U> inline bool chmax(T &a, const U &b){if(a<b){a=b;return 1;}return 0;}
template<class T,class U> inline bool chmin(T &a, const U &b){if(a>b){a=b;return 1;}return 0;}

const ld Pi = std::acos(-1.0L);
constexpr ll infll = (1LL<<62)-1;
constexpr int inf = (1<<30)-1;
const int mod = 1000000007;
// const int mod = 998244353;

/*MOD int=============================*/
template<std::int_fast64_t Mod>
class modint {
    using i64 = std::int_fast64_t;
public:
    i64 val;
    //constructor
    constexpr modint(const i64 p=0) noexcept : val(p>=0 ? p%Mod : (Mod+(p%Mod))%Mod) {}

    //std::cin, std::cout
    friend std::ostream &operator<<(std::ostream &os, const modint &x) {
        return os << x.val;
    }
    friend std::istream &operator>>(std::istream &is, modint &x) {
        is >> x.val;
        x.val %= Mod;
        if(x.val < 0) x.val += Mod;  // <- 負数対応
        return is;
    }

    //operator
    constexpr modint operator+(const modint b) const noexcept { return modint(*this) += b; }

    constexpr modint operator-(const modint b) const noexcept { return modint(*this) -= b; }

    constexpr modint operator*(const modint b) const noexcept { return modint(*this) *= b; }

    constexpr modint operator/(const modint b) const noexcept { return modint(*this) /= b; }

    constexpr modint operator-() const noexcept { return modint() - *this; }

    constexpr bool operator==(const modint &b) const noexcept { return this->val == b.val; }

    constexpr bool operator!=(const modint &b) const noexcept { return this->val != b.val; }

    constexpr modint &operator=(const modint b) noexcept {
        val = b.val;
        return *this;
    }
    constexpr modint &operator=(const i64 b) noexcept {
        val = modint<Mod>(b).val;
        return *this;
    }
    constexpr modint &operator+=(const modint b) noexcept {
        if((val += b.val) >= Mod) val -= Mod;
        return *this;
    }
    constexpr modint &operator-=(const modint b) noexcept {
        if(val < b.val) val += Mod;
        val -= b.val;
        return *this;
    }
    constexpr modint &operator*=(const modint b) noexcept {
        val = val * b.val % Mod;
        return *this;
    }
    constexpr modint &operator/=(modint b) noexcept {
        val *= b.inverse().val;
        val %= Mod;
        return *this;
    }
    constexpr modint inverse() noexcept {
        i64 m=Mod, u=1, v=0, t=1;
        while(m) {
            t = val/m;
            val -= t*m; std::swap(val,m);
            u -= t*v; std::swap(u,v);
        }
        return modint(u);
    }
    // calc val^n
    constexpr  modint pow(i64 n) noexcept {
        modint res = 1, a = val;
        while(n > 0) {
            if(n & 1) res = res * a;
            a = a * a;
            n >>= 1;
        }
        return res;
    }
};
using mint = modint<mod>;

/*FUNCs=================================================*/


/*MAIN==================================================*/
signed main(){
    int START_TIME = clock();
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
//    cout << fixed << setprecision(15);

    i32 n,m; cin >> n >> m;
    vec<bool> x(1e5+10);
    rep(i,m) {
        i32 tmp;
        cin >> tmp;
        x[tmp] = true;
    }

    vec<mint> dp(n+10);
    dp[0] = 1;
    for(i32 i = 0; i < n; ++i) {
        if(x[i]) continue;
        if(!x[i+1]) dp[i+1] += dp[i];
        if(!x[i+2]) dp[i+2] += dp[i];
    }

    cout << dp[n] << '\n';

    // printf("ExecutionTime: %d /ms\n",1000*(int)((clock()-START_TIME)/CLOCKS_PER_SEC));
}