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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func calc(N int, am map[int]struct{}) int64 {
	dp := make([]int64, N+1)
	dp[0] = 1
	dp[1] = 1
	if _, ok := am[1]; ok {
		dp[1] = 0
	}

	for i := 2; i <= N; i++ {
		if dp[i-1] == 0 && dp[i-2] == 0 {
			break
		}

		dp[i] = (dp[i-1] + dp[i-2]) % 1000000007
		if _, ok := am[i]; ok {
			dp[i] = 0
		}
	}

	return dp[N]
}

func main() {
	var N, M int
	fmt.Scanf("%d %d", &N, &M)
	am := map[int]struct{}{}
	for i := 1; i <= M; i++ {
		var a int
		fmt.Scan(&a)
		am[a] = struct{}{}
	}

	ans := calc(N, am)
	fmt.Println(ans % 1000000007)
}