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)


#coding:utf-8

from functools import reduce
import fractions

n, x = map(int, input().split(' '))
nums = list(map(int, input().split(' ')))

def devide_cnt(num):
    cnt = 0
    while num % 2 == 0:
        cnt += 1
        num //= 2
    return cnt, num

def lcm_base(x, y):
    return (x * y) // fractions.gcd(x, y)

def lcm(*numbers):
    return reduce(lcm_base, numbers, 1)

def lcm_list(numbers):
    return reduce(lcm_base, numbers, 1)


def main():
    odd_nums = []
    cnt = -1
    for num in nums:
        tmp, num = devide_cnt(num)
        if cnt == -1:
            cnt = tmp
        if cnt != tmp:
            print(0)
            return
        odd_nums.append(num)
        
    minv = 2 ** cnt * lcm_list(odd_nums)

    
    l = 1
    r = 10000000001
    tmp = -1
    while l < r + 1:
        m = l + (r - l) // 2
        p = m * minv + 0.5 * minv
        if p > x:
            r = m
        else:
            l = m
        
        if tmp == p:
            break
        tmp = p
        
            
    print(l+1)
    
    
    

main()