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: Accepted)

package main

import (
	"fmt"
)

func main() {
	var n, m int
	fmt.Scanf("%d %d\n", &n, &m)

	var x int
	a := makeTrueSlice(n+1)
	for i := 0; i < m; i++ {
		fmt.Scanf("%d", &x)
		a[x] = false}

	fmt.Println(resolve(n, a))
}

func resolve(n int, a []bool) int {
	dp := make([]int, n+1)
	dp[0] = 1
	
	mod := 1000000007
	for i := 1; i <= n; i++ {
		if a[i] {
			switch i {
			case 1:
				dp[i] = 1
				break
			default:
				dp[i] = (dp[i-1] + dp[i-2])%mod
			}
		}
	}
	return dp[n]
}

func makeTrueSlice(len int) []bool {
	slice := make([]bool, len)
	for i := 0; i<len; i++ {
		slice[i] = true
	}
	return slice
}