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: Runtime Error)

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 sum(array []int, start int, end int) int {
	ret := 0
	for i := start; i < end; i++ {
		ret += array[i]
	}
	return ret
}

func factorial(n uint64) uint64 {
	var ret uint64
	var i uint64
	ret = 1
	for i = 1; i <= n; i++ {
		ret *= i
	}

	//fmt.Printf("factorial: %d = %d\n", n, ret)
	return ret
}

func calc(steps uint64) uint64 {
	max := steps / 2
	//fmt.Printf("steps: %d max: %d\n", steps, max)

	var step1 uint64
	var step2 uint64
	var ret uint64
	ret = 0
	for step2 = 0; step2 <= max; step2++ {
		step1 = steps - (step2 * 2)

		if step2 == 0 {
			ret++
			continue
		}
		if step1 == 0 {
			ret++
			continue
		}
		ret += (factorial(step1+step2) / (factorial(step1) * factorial(step2)))
	}
	//fmt.Printf("calc: %d\n", ret)
	return ret
}

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

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

	finished := false
	var sum uint64
	sum = 1

	for index, b := range broken {
		// no way to reach
		if index < len(broken)-1 && broken[index+1] == b+1 {
			fmt.Println(0)
			finished = true
			break
		}

		startIndex := 0
		if index > 0 {
			startIndex = broken[index-1] + 1
		}
		//fmt.Printf("start: %d end:%d\n", startIndex, b-1)
		sum *= calc(uint64(b - 1 - startIndex))
	}

	if finished {
		return
	}

	if len(broken) > 0 && broken[len(broken)-1] < n-1 {
		sum *= calc(uint64(n - 1 - broken[len(broken)-1]))
	}

	if len(broken) == 0 {
		sum *= calc(uint64(n))
	}

	fmt.Println(sum % 1000000007)
}