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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
typedef long long ll;

const ll mod = (ll)(1e9) + 7;

ll n, m;
ll a;
ll dp[100005];

ll solve(ll i);

int main()
{
    for (int i = 0; i < 100005; i++) {
        dp[i] = -1;
    }

    scanf("%lld %lld", &n, &m);
    for (int i = 0; i < m; i++) {
        scanf("%lld", &a);
        dp[a] = 0;
    }

    printf("%lld\n", solve(0));

    return 0;
}

ll solve(ll i)
{
    if (dp[i] != -1) {
        return dp[i];
    }
    if (i == n) {
        return 1;
    }
    if (i > n) {
        return 0;
    }

    return dp[i] = (solve(i + 1) + solve(i + 2)) % mod;
}