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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import java.math.*;
import java.lang.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int n = sc.nextInt();
		int m = sc.nextInt();
		List<Integer> list = new ArrayList<>();
		long result = 1;
		long CONST_BIG_VALUE = 1000000007l;
		long currentPattern =0;
		Map<Integer, Long> cash = new HashMap<>();

		int prevA =0;

		for (int i = 0; i < m; i++) {
			int a = sc.nextInt();
			list.add(a-prevA);
			prevA =a;
		}
		list.add(n-prevA);

		for (int i = 0; i <= m; i++) {
			int currentDistance = list.get(i);
			if (currentDistance == 1 && i!=0) {
				result = 0;
				// System.out.println("currentDistance 0 case ");
				break;
			}

			if(cash.containsKey(currentDistance-1)){
				result = (result * cash.get(currentDistance-1)) % CONST_BIG_VALUE;
			}else{
				long cashed = calcPattern(currentDistance-1);
				cash.put(currentDistance-1,cashed);
				result = (result * cashed) % CONST_BIG_VALUE;
			}
			// System.out.println("currentDistance-1 " + (currentDistance-1));
			// System.out.println("result " + result);
		}
		System.out.println(result);

	}

	private static long calcPattern(int distance){
		if(distance == 0){
			return 1;
		}
		if(distance == 1){
			return 1;
		}
		long result = 0;
		boolean flag =true;
		int childDistance =distance;

		while(flag){
			if(childDistance<0){
				flag =false;
				break;
			}
			result += calcNumOfCombination(distance, childDistance);
			// System.out.println("calcPattern distance " + distance);
			// System.out.println("calcPattern childDistance " + childDistance);
			// System.out.println("calcPattern result " + result);
			distance--;
			childDistance -= 2;
		}

		// System.out.println("calcPattern result " + result);
		return result;
	}

	private static long calcNumOfCombination(int n, int r){
		long num = 1;
		if(r==0){
			return 1;
		}
		r = Math.min(r,n-r);
        for(int i = 1; i <= r; i++){
            num = factorialUp(n,r)/factorial(r);
        }
		// System.out.println("calcNumOfCombination n " + n);
		// System.out.println("calcNumOfCombination r " + r);
		// System.out.println("calcNumOfCombination num " + num);
        return num;
	}
	
	private static long factorial(long n){
		if(n<0){
			return n;
		}
		if(n==0){
			return 1;
		}
		return n * factorial(n-1);
	}

	private static long factorialUp(int n, int r){
		long result = 1;
		for(int i=0;i<r;i++){
			result = result * (n-i);
		}
		return result;
	}

}