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"
)

func product(l []int) int {
	s := 1
	for _, x := range l {
		s = x * s % 1000000007
	}
	return s
}

func fib(n int) int {
	f1 := 2
	f2 := 1
	temp := 1
	ans := 0
	if n <= 2 {
		if n == 0 {
			return 1
		}
		if n == 1 {
			return 1
		}
		return 2
	}
	for i := 3; i <= n; i++ {
		ans = f1 + f2
		temp = f2
		f2 = f1
		f1 = temp + f1
	}
	return ans
}

func contains(s []int, e int) bool {
	for _, v := range s {
		if e == v {
			return true
		}
	}
	return false
}

func main() {
	var n, m int
	fmt.Scan(&n, &m)
	a := make([]int, m+2)
	a[0] = -1
	for i := 1; i <= m; i++ {
		fmt.Scan(&a[i])
	}
	a[m+1] = n + 1
	d := make([]int, m+1)
	for i := 0; i < m+1; i++ {
		d[i] = a[i+1] - a[i] - 2
	}
	if contains(d, -1) {
		fmt.Println(0)
	} else {
		for i := 0; i < m+1; i++ {
			d[i] = fib(d[i])
		}
		fmt.Println(product(d))
	}
}