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"
)

const MOD = 1000000007

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

	var as []int
	for i := 0; i < M; i++ {
		fmt.Scan(&a)
		as = append(as, a)
	}

	res := 1
	for i := 0; i < M; i++ {
		n := 0
		if i == 0 {
			n = as[i] - 1
		} else {
			n =  as[i] - as[i - 1] - 2
		}

		if n < 0 {
			fmt.Println(0)
			return
		}

		res *= fib(n) % MOD
		res = res % MOD
	}

	if M > 0 {
		res *= fib(N-as[M-1]-1) % MOD
		res = res % MOD
	} else {
		res *= fib(N) % MOD
	}

	fmt.Println(res)
}

func fib(N int) int {
	if N < 2 {
		return 1
	}

	n1, n2, f := 1, 1, 1

	for i := 0; i < N - 1; i++ {
		f = n1 + n2
		n1 = n2
		n2 = f
	}

	return f
}