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)

import functools
import sys

n, m = map(int, input().split())
a = list(map(lambda x: x // 2, map(int, input().split())))
a = set(a)

# A[0]を素因数分解して2で割り切れる回数を数える
div = 0

a_0 = a[0]
while a_0 % 2 == 0:
    a_0 /= 2
    div += 1

# print("count = " + str(div))#

# Aのすべての整数がA[0]と同じ回数2で割り切れるか調べる
for i in range(1, len(a)):
    div2 = 0
    a = a[i]
    while a % 2 == 0:
        a /= 2
        div2 += 1
    # print("A[" + str(i) + "] count = " + str(div2))#
    if div2 != div:
        print("0")
        sys.exit()


def gcd(x, y):
    if x == 0:
        return y

    return gcd(y % x, x)


def least_common_multiple(iter):
    '''
    最小公倍数を返す
    '''
    lcm = lambda x, y: x * y // gcd(x, y)
    return functools.reduce(lcm, iter)


lc = least_common_multiple(a)
ans = 0
a = 1

ans = m // lc
if ans == 0:
    print(0)
    sys.exit()
if ans % 2 == 0:
    print(ans // 2)
else:
    print(ans // 2 + 1)