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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using static System.Math;using static System.Console;using System.Collections.Generic;using System.Linq;using System;using System.Collections;
using System.Runtime.Serialization;
using System.Collections.Specialized;
using System.Security.Cryptography;
using System.Globalization;

class Program
{
    #region Reader
    static string ReadStr => Console.ReadLine();
    static string[] ReadStrs => Console.ReadLine().Split(' ');
    static int ReadInt => Convert.ToInt32(Console.ReadLine());
    static int[] ReadInts => Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    static long ReadLong => Convert.ToInt64(Console.ReadLine());
    static long[] ReadLongs => Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    #endregion
    #region Method
    const int mod = 1000000007;
    public static int Mod(int a,int mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    public static long Mod(long a, int mod = mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    #endregion


    #region Mod
    public static long GetInv(long a, long mod = 1000000007)
    {
        return PowerMod(a, mod - 2, mod);
    }
    public static long Combination(long a, long b, long mod = 1000000007)
    {
        if (b < 0 || b > a) return 0;
        if (b > a / 2) b = a - b;
        long numerator = Factorial(a, mod);
        long denominator = (Factorial(b, mod) * Factorial(a - b, mod)) % mod;

        return (numerator * GetInv(denominator, mod)) % mod;
    }
    public static long Factorial(long n, long mod = 1000000007)
    {
        if (n == 0) return 1;
        if (n == 1) return 1;
        long ans = n;
        for (int i = 2; i < n; i++)
        {
            ans = (ans * i) % mod;
        }

        return ans;
    }
    private static long PowerMod(long a, long n, long mod = 1000000007)
    {
        if (n == 0) return 1;
        if (n == 1) return a;

        long p = PowerMod(a, n / 2, mod);
        if (n % 2 == 1) return ((p * p) % mod * a) % mod;
        else return (p * p) % mod;
    }
    #endregion

    /// <summary>
    /// 最小公倍数
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }


    /// <summary>
    /// 最大公約数
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }

    public static Dictionary<int, int> PrimeFactors(int n)
    {
        int i = 2;
        int tmp = n;
        Dictionary<int, int> d = new Dictionary<int, int>();

        while (i * i <= n) //※1
        {
            if (tmp % i == 0)
            {
                tmp /= i;
                if (d.ContainsKey(i)) d[i]++;
                else d.Add(i, 1);
            }
            else
            {
                i++;
            }
        }
        if (tmp != 1)
        {
            if (d.ContainsKey(tmp)) d[tmp]++;
            else d.Add(tmp, 1);
        }
        return d;
    }


    static void Main()
    {
        long[] NM = ReadLongs;
        long N = NM[0];
        long M = NM[1];

        int[] As = new int[N];
        int[] vs = ReadInts;
        for (int i = 0; i < N; i++)
        {
            As[i] = vs[i] / 2;
        }

        var d0 = PrimeFactors(As[0]);
        int fact2 = d0.ContainsKey(2)?d0[2]:0;
        for (int i = 1; i < N; i++)
        {
            int count = 0;
            int temp = As[i];
            while (temp%2 == 0)
            {
                temp /= 2;
                count++;
            }

            if (fact2 != count)
            {
                WriteLine(0);
                return;
            }
        }

        long lcm = As[0];
        for (int i = 1; i < N; i++)
        {
            lcm = Lcm(As[i], lcm);
        }

        WriteLine((M / lcm) % 2 == 0 ? M / (2 * lcm) : M / (2 * lcm) + 1);
    }

}