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 Python (3.4.3) (judge verdict: Runtime Error)

from collections import deque

n,m=map(int,input().split())
l=list(map(int,input().split()))
l=[i/2 for i in l]
if n==1:
  if (m//l[0])%2==0:
    print(int((m//l[0])/2))
  else:
    print(int((m//l[0]+1)/2))
  exit()
def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a

l=set(l)
a1=l.pop()
a2=l.pop()
g=gcd(a1,a2)
lcm=g*(a1/g)*(a2/g)
d=1
while l:
  a=l.pop()
  d=gcd(g,a)
  lcm=d*(a/d)*(g/d)
  g=lcm
  

if lcm>m:
  print(0)
  exit()
for a in l:
  if (lcm/a)%2==0:
    print(0)
    break
else:
  if (m//lcm)%2==0:
    print(int((m//lcm)/2))
  else:
    print(int((m//lcm+1)/2))