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 Data.List

main = do
   [n,m] <- map (read) . words <$> getLine :: IO [Int]
   as <- map (half . read) . words <$> getLine :: IO [Int]
   putStrLn $ show (ans m as)

ans :: Int -> [Int] -> Int
ans m as = f (foldl1 (lcm1 m) as) m

lcm1 :: Int -> Int -> Int -> Int
lcm1 m a b
  | lcm a b > m = m+1
  | otherwise = lcm a b

half :: Int -> Int
half a = a `div` 2

f :: Int -> Int -> Int
f a m = (m + a) `div` (2 * a)