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 Lua (5.3.2) (judge verdict: Accepted)

local function getgcd(x, y)
  while 0 < x do
    x, y = y % x, x
  end
  return y
end

local function getlcm(x, y)
  local gcd = getgcd(x, y)
  return (x // gcd) * y
end

local n, m = io.read("*n", "*n")
local a = {}
for i = 1, n do
  a[i] = io.read("*n") // 2
end
local valid = true
local cur = a[1]
for i = 2, n do
  local gcd = getgcd(cur, a[i])
  if (cur // gcd) % 2 == 0 or (a[i] // gcd) % 2 == 0 then
    valid = false
    break
  end
  cur = (cur // gcd) * a[i]
  if m < cur then
    valid = false
    break
  end
end
if valid then
  local c = m // cur
  print(math.ceil(c / 2))
else
  print(0)
end