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: Wrong Answer)

import sys
import fractions
import copy

n, m = map(int, input().split())

if n == 1:
    A = int(input())
    if m%A != 0:
        print(int(m/A)+1)
    else:
        print(int(m/A))
    sys.exit()

A = [int(x) for x in input().split()]

if (A[0]/2)%2 == 0:
    B = [x/2 for x in A if (x/2)%2 == 0]
else:
    B = [x/2 for x in A if (x/2)%2 == 1]

if len(A) != len(B):
    print(0)
    sys.exit()

A = list(set(A))
mx = max(A)

skbs = B[0]
for i in range(1, len(B)):
    skbs = skbs * B[i] // fractions.gcd(skbs, B[i])

print(int(m/skbs/2)+1)

"""
start = int(mx/2)
ans = 0
for tm in range(start, m, 2):
    flag = 1
    for i in range(len(A)):
        if float(int(tm/A[i])) == float(tm/A[i]) - 0.5:
            continue
        else:
            flag = 0
            break
    if flag == 1:
        ans = tm
        break

hkbs = 0
a1, a2 = 0, 0
for ttm in range(ans, m, ans):
    flag = 1
    for i in range(len(A)):
        if float(int(ttm/A[i])) == float(ttm/A[i]) - 0.5:
            continue
        else:
            flag = 0
            break
    if flag == 1:
        hkbs += 1
        if hkbs == 1:
            a1 = ttm
        elif hkbs == 2:
            a2 = ttm
            break

if hkbs <= 1:
    print(hkbs)
else:
    print(int((m-ans)/(a2-a1))+1)
"""