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 (7.3.0) (judge verdict: Wrong Answer)

N,M=map(int, input().split())
from collections import defaultdict
A=list(map(int, input().split()))
B=[]
import math
def lcm(x, y):
    return (x * y) // math.gcd(x, y)
# a 偶数
twos=0
D=defaultdict(int)
for i in range(N):
    B.append(A[i]//2)
    a=A[i]
    now=0
    while a%2==0:
        a//=2
        now+=1
    D[now]+=1
    twos=max(twos, now)
if len(set(D.values()))!=1:
    print(0)
    exit()
now=1
for i in range(N):
    now=lcm(now, B[i])

# 1.5 * 3 2*5
from math import ceil

ans=M//(now*2)+1


print(ans)