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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>

uint64_t calcComb(int pre,int post){
    uint64_t temp =pre;
    int temppost = pre-post;
    if(temppost < post){
        post = temppost;
    }

    for(int k=1;k<post;k++){
        temp= temp * (pre-k);
    }
    for(int k=post;k>1;k--){
        temp = temp/k; 
    }
    return temp;
}


int main(){

    int N,M;
    int am[100000];

    std::cin>>N>>M;

    int none =0;

    if(M!=0){
        std::cin >> am[0];
    }

    for(int i=1;i<M;i++){
        std::cin >> am[i];
        if(am[i-1] == am[i]-1){none =1;}
    }
    if(none==1){
        std::cout<<0<<std::endl;
        return 0;
    }

    am[M] = N+1;
    M=M+1;

    uint64_t retnum=1;
    int pre =0;
    for(int i = 0;i<M;i++){
        int temp = am[i] - pre-1;
        if(temp>1){
            uint64_t bufnum=1;
            temp -=2;
            for(int j=1;;j++){
                if(temp==0){bufnum++;}
                else{
                    bufnum+= calcComb(temp+j,j);
                }
                temp-=2;
                if(temp <0){
                    break;
                }
            }
            retnum*= bufnum;
        }
        pre = am[i]+1;
    }

    retnum = retnum % 1000000007;

    std::cout << retnum <<std::endl;
}