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: Wrong Answer)

import sys, math
def input():
    return sys.stdin.readline()[:-1]
from itertools import permutations, combinations
from collections import defaultdict, Counter
d = defaultdict(int)

sys.setrecursionlimit(10**7)
N, M = map(int, input().split())
A = list(map(int, input().split()))

A = list(set(A))

def fctr1(n): 
    f=[]
    c=0
    r=int(n**0.5)
    for i in range(2,r+2):
        while n%i==0:
            c+=1
            n=n//i
        if c!=0:
            f.append([i,c])
            c=0
    if n!=1:
        f.append([n,1])
    return f

A_fac = [fctr1(val) for val in A]

max2 = max([val[0][1] for val in A_fac])

for vals in A_fac:
    for val in vals:
        if val[0] == 2: continue
        d[val[0]] = max(d[val[0]], val[1])

lcm = 1
lcm *= (2**max2)
for key, val in d.items():
    lcm *= (key**val)

div = M//lcm

if div + (lcm//2) <= M:
    print(div+1)
else:
    print(div)