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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List

main = do
  li <- getLine
  let [n,m] = map read $ words li
  li <- getLine
  let as = map read $ words li
  let ans = compute n m as
  print ans

{-
aは偶数なので2で割ってそれらのlcmを求めて、
その定数倍であって、全てのaiに対して kl/ai が奇数であるようなものを数えたい

もしl/aiが偶数だったら、kをいくつにしてもkl/aiは偶数
そんなときの答えは0個、そうでないときはつまり奇数なので、
m/lまでのkで奇数の個数だから、m/l+1/2 かな？

-}
compute :: Int -> Int -> [Int] -> Int
compute n m as
  | any (even . div l) bs = 0
  | True = (m `div` l + 1) `div` 2
  where
    bs = map (flip div 2) as
    l = foldl' lcm 1 bs