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)

#######################################
def csi(s=gets,spst=" ")
  if s==nil
    return 0
  end
  return s.chomp.split(spst).map(&:to_i)
end
def css(s=gets,spst=" ")
  if s == nil
    raise "nil!"
  end
  return s.chomp.split(spst).map(&:to_s)
end
def ml(n,datatype=:int)
  t = []
  case datatype
  when :int
    n.times do
      t.push(gets.to_i)
    end
  when :str
    n.times do
      t.push(gets.chomp.to_s)
    end
  else
    raise "n!"
  end
end
#######################################

n,m = csi
a = csi
n = n-1

ans = []

(1..m).to_a.select{|i|n%5==0}.each do |i|
  (0..n-1).to_a.select{|i|n%2==0}.each do |ii|
    if (i/ii.to_f-0.5) > 0 && (i/ii.to_f-0.5)%1==0
      ans.push(i)
    end
  end
end

puts ans.length