Problem:
Score : 400 points

Problem Statement

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).

Sample Input 1

2 50
6 10

Sample Output 1

2

15 = 6 \times 2.5

15 = 10 \times 1.5

45 = 6 \times 7.5

45 = 10 \times 4.5

Thus, 15 and 45 are semi-common multiples of A. There are no other semi-common multiples of A between 1 and 50, so the answer is 2.

Sample Input 2

3 100
14 22 40

Sample Output 2

0

The answer can be 0.

Sample Input 3

5 1000000000
6 6 2 6 2

Sample Output 3

166666667

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

# exec(open('test.py').read()) 
import math
import sys
 
N,M = map(int, input().split())
l = list(map(int, input().split()))
l.sort()

def lcm(a,b):
	return (a*b)//math.gcd(a,b)

def LCM(l):
	if max(l)//2 > M:
		print(0)
		exit(0)
	val = l[0]//2
	for j in range(1,N):
		if val < M:
			val = lcm(val,l[j]//2)
		else:
			return 0
	return val

gcf = LCM(l)

def isSCF(l):
	for x in l:
		if (gcf//(x//2))%2 == 0:
			return False
	return True

ans = 0

if isSCF(l):
	y = M//gcf
	if y%2 == 0:
		ans = y//2
	else:
		ans =(y+1)//2

if gcf == 0:
	print(0)
else:
	print(ans)