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 Ruby (2.3.3) (judge verdict: Wrong Answer)

$debug = false
flag = ARGV.shift
if flag == "-d"
  $debug = true
end

def dputs str
  p str if $debug
end

def max(n, m)
  if n > m
    return n
  else
    return m
  end
end

def min(n, m)
  if n < m
    return n
  else
    return m
  end
end

def gets_all_int
  return gets.chomp.split.map{|v| v.to_i}
end

## start

N, M = gets_all_int
as = gets_all_int

def half_common_multiple(ak, p)
  return (ak * (p + 0.5)).to_i
end

ary = []

as.each do |ak|
  p = 1
  ak_ary = []
  loop do
    hcm = half_common_multiple(ak, p)
    break if hcm > M
    dputs "#{ak} *| #{p} => #{hcm} < #{M}"
    ak_ary << hcm
    p += 1
  end

  if ary.empty?
    ary = ak_ary
  else
    ary &= ak_ary
  end
end

puts ary.length