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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var scanner = bufio.NewScanner(os.Stdin)

func next() string {
	scanner.Scan()
	return scanner.Text()
}

func nextInt() int {
	i, _ := strconv.Atoi(next())
	return i
}

func nextInts(n int) []int {
	ints := make([]int, n)
	for i := 0; i < n; i++ {
		ints[i] = nextInt()
	}
	return ints
}

func calc(n int) int {
	if n == 0 || n == 1 {
		return 1
	}

	if n == 2 {
		return 2
	}

	return calc(n-2) + calc(n-1)
}

func main() {
	scanner.Split(bufio.ScanWords)

	n := nextInt()
	m := nextInt()
	brokenSteps := nextInts(m)

	if n == 1 {
		fmt.Println(1)
		return
	}

	if n == 2 {
		if len(brokenSteps) == 0 {
			fmt.Println(2)
			return
		}
		fmt.Println(1)
		return
	}

	start := 0
	var answer uint64
	answer = 1
	for _, i := range brokenSteps {
		steps := i - start - 1
		if steps < 0 {
			fmt.Println(0)
			os.Exit(0)
		}
		answer *= uint64(calc(steps))
		start = i + 1
	}

	if start < n {
		steps := n - start
		answer *= uint64(calc(steps))
	}

	fmt.Println(answer % 1000000007)
}