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: Wrong Answer)

import Control.Monad
main = print =<< ((pure ans) <*> getInput)

getInts :: IO [Integer]
getInts = (pure ((map read) . words)) <*> getLine

getInput :: IO [[Integer]]
getInput = replicateM 2 getInts

{-
gcd :: Integer -> Integer -> Integer
gcd a 0 = a
gcd a b = gcd b $ mod a b

lcm :: Integer -> Integer -> Integer
lcm a b = div (a * b) $ gcd a b
-}

lcmList :: Integer -> [Integer] -> Integer
lcmList m = foldl (\a b -> if b > m then m + 1 else lcm a b) 1

ans :: [[Integer]] -> Integer
ans [[n, m], a] = (`div` 2) $ (+) 1 $ div m $ (`div` 2) $ lcmList m a