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 Python (3.4.3) (judge verdict: Runtime Error)

import sys
from fractions import gcd
inputs = sys.stdin.readlines()

n, m = map(int, inputs[0].split())
A = list(set(map(int, inputs[1].split())))
B = list(map(lambda x: x//2, A))

prod_A = gcd_A = A[0]
for a in A[1:]:
    gcd_A = gcd(gcd_A, a)
    prod_A *= a
sup = prod_A // gcd_A

C = []
for b in B:
    p, x, c = 0, b*1, {0}
    while x <= sup:
        c.add(x)
        p += 2
        x = b*(p + 1)
    sup = max(c)
    C.append(c)
    
cap_c = C[0]
for c in C[1:]:
    cap_c &= c
cap_c.discard(0)
if not c:
    print(0)
else:
    print((m // min(cap_c) + 1) // 2)