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)

#from math import sqrt
#from heapq import heappush, heappop
#from collections import deque
from functools import reduce

#a, b = [int(v) for v in input().split()]


def main():
    N, M = [int(v) for v in input().split()]
    A = list(set([int(v) for v in input().split()]))

    def calc(v1, v2):
        while v1 % v2 != 0:
            tmp = v2
            v2 = v1 % v2
            v1 = tmp
        return v2

    min_a = reduce(lambda v1, v2: v1 // 2 * v2 //
                   2 // calc(v1 // 2, v2 // 2), A)

    if M * 2 < min_a:
        print(0)
    else:
        print((M - min_a) // (min_a * 2) + 1)


main()