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"

var memo map[int]int

func stepupN(n int) int {
	if n < 0 {
		return 0
	}
	if n == 0 {
		return 1
	} else if memo[n] > 0 {
		return memo[n]
	} else {
		memo[n] = stepupN(n-1) + stepupN(n-2)
	}
	return memo[n] % 1000000007
}

func main() {
	var n, m int
	fmt.Scan(&n, &m)
	memo = make(map[int]int, n)
	memo[1] = 1
	memo[2] = 2
	w := make([]int, m)
	for i := range w {
		fmt.Scan(&w[i])
		if i > 0 {
			if w[i-1]+1 == w[i] { //連続して壊れている
				fmt.Println(0)
				return
			}
		}
	}
	w = append(w, n+1)
	// 連続して壊れている階段はない
	// 壊れている階段で分けられる複数の階段を考える
	var oks, steps, bads int
	ans := 1
	for i := 0; i < len(w); i++ {
		// w[i] 壊れている階段
		if bads == w[i] {
			continue
		}
		steps = w[i] - oks - 1
		bads = w[i]
		oks = w[i] + 1
		//fmt.Println("i", i, "steps", steps, "oks", oks)
		ans = (ans * stepupN(steps)) % 1000000007
	}
	fmt.Println(ans)
}