Problem: Given are a sequence A= {a_1,a_2,......a_N} of N positive even numbers, and an integer M.

Let a semi-common multiple of A be a positive integer X that satisfies the following condition for every k (1 \leq k \leq N):

* There exists a non-negative integer p such that X= a_k \times (p+0.5).



Find the number of semi-common multiples of A among the integers between 1 and M (inclusive).

Constraints

* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^9
* 2 \leq a_i \leq 10^9
* a_i is an even number.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
a_1 a_2 ... a_N


Output

Print the number of semi-common multiples of A among the integers between 1 and M (inclusive).

Examples

Input

2 50
6 10


Output

2


Input

3 100
14 22 40


Output

0


Input

5 1000000000
6 6 2 6 2


Output

166666667

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Main {
	static int mod = (int) 1e9 + 7;
	static int DX[] = { -1, 0, 1, 0 }, DY[] = { 0, -1, 0, 1 };
	static final int INF = Integer.MAX_VALUE / 3;
	static final long LINF = Long.MAX_VALUE / 3;

	public static void main(String[] args) {
		FastScanner fs = new FastScanner(System.in);
		int n = fs.nextInt(), m = fs.nextInt();
		int a[] = fs.nextIntArray(n);

		for(int i=0;i<n;i++) {
			a[i] /= 2;
		}
		
		int cnt = 1;
		while(a[0]%(cnt*2)==0) {
			cnt *= 2;
		}
		for(int i=1;i<n;i++) {
			if(a[i]%cnt!=0||a[i]/cnt%2==0) {
				System.out.println(0);
				return;
			}
		}
		
		long l = 1;
		for(int i=0;i<n;i++) {
			l = lcm(a[i], l);
			if(l>m) {
				System.out.println(0);
				return;
			}
		}
		
		long mp = m / l;
		
		long ans = (mp+1)/2;
		System.out.println(ans);
		
	}

	static long gcd(long x, long y) {
		return y == 0? x : gcd(y, x%y);
	}
	static long lcm(long x, long y) {
		return x / gcd(x, y) * y;
	}
	
	
	//MOD culculations
	static long plus(long x, long y) {
		long res = (x + y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long sub(long x, long y) {
		long res = (x - y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long mul(long x, long y) {
		long res = (x * y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long div(long x, long y) {
		long res = x * pow(y, mod - 2) % mod;
		return res < 0 ? res + mod : res;
	}

	static long pow(long x, long y) {
		if (y < 0)
			return 0;
		if (y == 0)
			return 1;
		if (y % 2 == 1)
			return (x * pow(x, y - 1)) % mod;
		long root = pow(x, y / 2);
		return root * root % mod;
	}
}

//高速なScanner
class FastScanner {
	private BufferedReader reader = null;
	private StringTokenizer tokenizer = null;

	public FastScanner(InputStream in) {
		reader = new BufferedReader(new InputStreamReader(in));
		tokenizer = null;
	}

	public String next() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	public String nextLine() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken("\n");
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}
}