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: Time Limit Exceeded)

	package main

	import "fmt"

	var mod int = 1000000007
	var N, M int
	var a []int
	var memo []int

	func main() {
		fmt.Scan(&N, &M)

		a = make([]int, N+1)
		for i := 0; i < M; i++ {
			var t int
			fmt.Scan(&t)
			a[t] = 1
		}
		memo = make([]int, N+1)
		fmt.Println(dfs(N))
	}

	func dfs(n int) int {
		if n < 0 || a[n] == 1 {
			return 0
		}
		if memo[n] != 0 {
			return memo[n]
		}
		if n == 0 {
			memo[0] = 1
			return memo[0]
		}
		var x, y int
		if 0 < n-1 && memo[n-1] != 0 {
			x = memo[n-1]
		} else {
			x = dfs(n - 1)
		}

		if 0 < n-2 && memo[n-2] != 0 {
			y = memo[n-2]
		} else {
			y = dfs(n - 2)
		}

		memo[n] = (x + y) % mod
		return memo[n]
	}