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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
sys.setrecursionlimit(10 ** 7)

'''
#import numpy as np
import math, string, itertools, fractions, heapq, collections, re, array, bisect, copy, functools, random
from collections import deque, defaultdict, Counter
from heapq import heappush, heappop
from itertools import permutations, combinations, product, accumulate, groupby
from bisect import bisect_left, bisect_right, insort_left, insort_right
from operator import itemgetter as ig
#sys.setrecursionlimit(10 ** 7)
'''
inf = 10 ** 20
'''
INF = float("INF")
mod = 10 ** 9 + 7
"""dd = [(-1, 0), (0, 1), (1, 0), (0, -1)];
ddn = dd + [(-1, 1), (1, 1), (1, -1), (-1, -1)];
ddn9 = ddn + [(0, 0)]
for dx, dy in dd:
        nx = j + dx; ny = i + dy
            if 0 <= nx < w and 0 <= ny < h:"""

def wi(): return list(map(int, sys.stdin.readline().split()))
def wip(): return [int(x) - 1 for x in sys.stdin.readline().split()]  # WideIntPoint
def ws(): return sys.stdin.readline().split()
def si(): return int(sys.stdin.readline())  # SingleInt
def ss(): return input()
def hi(n): return [si() for _ in range(n)]
def hs(n): return [ss() for _ in range(n)]  # HeightString
def s_list(): return list(input())
def mi(n): return [wi() for _ in range(n)]  # MatrixInt
def mip(n): return [wip() for _ in range(n)]
def ms(n): return [ws() for _ in range(n)]
def num_grid(n): return [[int(i) for i in sys.stdin.readline().split()[0]] for _ in range(n)]  # NumberGrid
def grid(n): return [s_list() for _ in range(n)]

def main():
'''
N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]
dp = [1] * N
if 1 in a:
    dp[0] = 0
    for i in range(1,N):
        if i+1 in a:
            dp[i] = 0
        else:
            dp[i] = dp[i-1] + dp[i-2]
    print(dp[N-1] % (10**9+7))
else:
    for i in range(1,N):
        if i+1 in a:
            dp[i] = 0
        else:
            dp[i] = dp[i-1] + dp[i-2]
    print(dp[N-1] % (10**9+7))

'''
if __name__ == '__main__':
    main()
'''