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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <limits.h>

#define ROOP(i,n) for(i=0;i<n;i++)

//prototype declaration
int getint();
long long getllint();
double getdint();
char getch();
void setstring(char *s);
void showint(int i);
void showllint(long long i);
void showdouble(double i);
void showchar(char c);
void showstring(char *s);

int myPower(int a, int n) { // aのn乗の計算
	int x = 1;
	while (n > 0) { // 全てのbitが捨てられるまで
		if ( n & 1) { // 一番右のbitが１のとき
			x *= a;
		}
		a *= a;
		n >>= 1; // bit全体を右に1つシフトして一番右を捨てる
	}
	return x;
}

int min(int a, int b) {
	return a < b ? a : b;
}

#define mod 1000000007
static int kaidan[10002] = {0};
static int64_t dp[10002];

int main(void) {
	int n, m, i;
	n = getint();
	m = getint();
	ROOP(i, m) {
		int a;
		a = getint();
		kaidan[a] = 1;
	}
	dp[0] = 1;
	if (kaidan[1] == 0) {
		dp[1] = 1;
	}
	for(i = 2;i <= n; i++) {
		if (kaidan[i] != 0) {
			dp[i] = 0;
			continue;
		}
		dp[i] = (dp[i - 1] + dp[i - 2]) % mod;
	}
	printf("%lld\n", dp[n]);
	return 0;
}

int getint() {
	int i;
	scanf("%d", &i);
	return i;
}

long long getllint() {
	long long i;
	scanf("%lld", &i);
	return i;
}

double getdint() {
	double i;
	scanf("%lf", &i);
	return i;
}

char getch() {
	char c;
	scanf("%c", &c);
	return c;
}

void setstring(char *s) {
	scanf("%s", s);
}

void showint(int i) {
	printf("%d\n", i);
}

void showllint(long long i) {
	printf("%lld\n", i);
}

void showdouble(double i) {
	printf("%lf\n", i);
}

void showchar(char c) {
	printf("%c\n", c);
}

void showstring(char *s) {
	printf("%s\n", s);
}