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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program semi_common_multiple
    implicit none
    integer(4):: n, m, i
    integer(4), allocatable:: a(:)
    integer(8):: gcd, lcm

    read*, n, m
    allocate(a(n))
    read*, a(:)
    a(:) = a(:) / 2

    do while(mod(a(1), 2) == 0)
        do i=1, n
            if(mod(a(i),2) /= 0) call die
            a(i) = a(i) / 2
        end do
        m = m / 2
    end do

    do i = 1, n
        if (mod(a(i), 2) == 0) call die
    end do

    lcm = 1

    do i=1,n
        gcd = calc_gcd(lcm,int(a(i),8))
        lcm = lcm/gcd*a(i)
    end do

    print*, (m/lcm+1_16)/2_16

contains
recursive function calc_gcd(a,b) result(ret)
integer(8):: a, b, ret
    if (mod(a,b) == 0)then
        ret = b
    else
    ret = calc_gcd(b,mod(a,b))
    endif
end function

subroutine die
    print*, 0
    stop
end subroutine
end program