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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    long m = sc.nextLong();
    long[] a = new long[n];
    for(int i = 0; i < n; i++ ) {
      a[i] = sc.nextLong();
    }

    Main abc150D = new Main();
    System.out.println(abc150D.solve(m, a));
  }

  public Long solve(long m, long[] a) {
    long multi = 1L;
    for(int i = 0; i < a.length; i++ ) {
      multi = multiplue(multi, a[i] / 2);
    }
    long ret = 0L;
    for(int i = 1; i <= m / multi; i++ ){
      if(i%2 == 1) {
        ret += 1L;
      }
    }
    return ret;
  }

  private long multiplue(long a, long b) {
    long ret = a > b ? a : b;
    long unit = a > b ? a : b;
    long base = a > b ? b : a;
    while(ret % base != 0) {
      ret += unit;
    }
    return ret;
  }
}