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: Wrong Answer)

package main

import "fmt"

var mod uint64 = 1000000007
var N, M int
var a []int
var memo []uint64

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

	a = make([]int, M)
	for i := 0; i < M; i++ {
		fmt.Scan(&a[i])
	}
	memo = make([]uint64, N+1)
	fmt.Println(dfs(0))
}

func dfs(n int) uint64 {
	if N < n {
		return 0
	}
	if memo[n] != 0 {
		return memo[n]
	}
	if n == N {
		return 1
	}

	for i := 0; i < M; i++ {
		if a[i] == n {
			return 0
		}
		if n < a[i] {
			break
		}
	}

	memo[n] = dfs(n+1) % mod
	memo[n] += dfs(n+2) % mod

	return memo[n]
}