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: Wrong Answer)

program semi_common_multiple
  implicit none
  integer :: n, i
  integer(8) :: m, a(100000) = 0, l = 1
  read(*,*) n, m
  read(*,*) a(1:n)
  do i = 1, n
    a(i) = a(i)/2
    l = lcm(l,a(i))
    if (l > m .or. mod(l,2) == 0) then
      write(*,'(i0)') 0
      stop
    end if
  end do
  write(*,'(i0)') (m/l+1)/2
contains
  integer(8) function lcm(a,b)
    integer(8), intent(in) :: a, b
    lcm = a/gcd(a,b)*b
  end
  integer(8) function gcd(a,b)
    integer(8), intent(in) :: a, b
    integer(8) :: x, y
    x = max(a,b)
    y = min(a,b)
    do while (y > 0_8)
      gcd = y
      y = mod(x,y)
      x = gcd
    end do
  end
end program semi_common_multiple