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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStreamReader
import java.io.PrintWriter
import kotlin.math.max
import kotlin.math.min

val br = BufferedReader(InputStreamReader(System.`in`))
val out = PrintWriter(System.out)

fun main() {
    br.use { out.use {
        solve()
        out.flush()
    } }
}

fun solve() {
    val (n, m) = readIntegerList()
    val dp = LongArray(n + 5)
    dp[0] = 1
    val breakSet = mutableSetOf<Int>()
    repeat(m) { breakSet.add(readInteger()) }
    val mod = 1000000007
    for (i in 0 until n) {
        dp[i + 1] = if (breakSet.contains(i + 1)) dp[i + 1] else (dp[i + 1] + dp[i]) % mod
        dp[i + 2] = if (breakSet.contains(i + 2)) dp[i + 2] else(dp[i + 2] + dp[i]) % mod
    }
    out.println(dp[n])
}

fun readInteger() = Integer.parseInt(br.readLine())
fun readLong() = java.lang.Long.parseLong(br.readLine())
fun readStringList() = br.readLine()!!.split(' ')
fun readIntegerList() = readStringList().map(Integer::parseInt)
fun readLongList() = readStringList().map(java.lang.Long::parseLong)
fun readDoubleList() = readStringList().map(java.lang.Double::parseDouble)