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# (Mono 4.6.2.0) (judge verdict: Accepted)

using AtCoderBeginnerContest150.Questions;
using AtCoderBeginnerContest150.Extensions;
using AtCoderBeginnerContest150.Algorithms;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Numerics;

namespace AtCoderBeginnerContest150.Questions
{

    public class QuestionD : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nm = inputStream.ReadIntArray();
            var n = nm[0];
            var m = nm[1];

            var a = inputStream.ReadIntArray();
            var halfA = a.Select(i => i / 2).ToArray();
            var lcm = new BigInteger(1);    // ゴリ押し

            var evenCount = f(halfA[0]);
            if (halfA.All(i => f(i) == evenCount))
            {
                halfA = halfA.Select(i => i / (1 << evenCount)).ToArray();
                foreach (var halfAi in halfA)
                {
                    lcm = BasicAlgorithms.Lcm(lcm, halfAi);
                }

                var count = (m / (lcm << evenCount) + 1) / 2;
                yield return count;
            }
            else
            {
                yield return 0;
            }

        }

        private int f(int n)
        {
            int count = 0;
            while (n % 2 == 0)
            {
                n /= 2;
                count++;
            }
            return count;
        }
    }
}


namespace AtCoderBeginnerContest150
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionD();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace AtCoderBeginnerContest150.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

namespace AtCoderBeginnerContest150.Algorithms
{
    public static class BasicAlgorithms
    {
        public static BigInteger Gcd(BigInteger a, BigInteger b)
        {
            if (a <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(a), $"{nameof(b)}は正の整数である必要があります。");
            }
            if (b <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(b), $"{nameof(b)}は正の整数である必要があります。");
            }
            if (a < b)
            {
                var temp = a;
                a = b;
                b = temp;
            }

            while (b != 0)
            {
                var temp = a % b;
                a = b;
                b = temp;
            }
            return a;
        }

        public static BigInteger Lcm(BigInteger a, BigInteger b)
        {
            if (a <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(a), $"{nameof(b)}は正の整数である必要があります。");
            }
            if (b <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(b), $"{nameof(b)}は正の整数である必要があります。");
            }

            return a / Gcd(a, b) * b;
        }

        public static IEnumerable<T[]> GetPermutations<T>(IEnumerable<T> collection, bool isSorted) where T : IComparable<T>
        {
            var a = collection.ToArray();

            if (!isSorted && a.Length > 1)
            {
                Array.Sort(a);
            }

            yield return a; // ソート済み初期配列

            if (a.Length <= 2)
            {
                if (a.Length == 2 && a[0].CompareTo(a[1]) != 0)
                {
                    var temp = a[0];
                    a[0] = a[1];
                    a[1] = temp;
                    yield return a;
                    yield break;
                }

                yield break;
            }

            bool flag = true;
            while (flag)
            {
                flag = false;
                for (int i = a.Length - 2; i >= 0; i--)
                {
                    // iよりi+1の方が大きい（昇順）なら
                    if (a[i].CompareTo(a[i + 1]) < 0)
                    {
                        // 後ろから見ていってi<jとなるところを探して
                        int j;
                        for (j = a.Length - 1; a[i].CompareTo(a[j]) >= 0; j--) { }

                        // iとjを入れ替えて
                        var temp = a[i];
                        a[i] = a[j];
                        a[j] = temp;

                        // i+1以降を反転
                        if (i < a.Length - 2)
                        {
                            Array.Reverse(a, i + 1, a.Length - (i + 1));
                        }

                        flag = true;
                        yield return a;
                        break;
                    }
                }
            }
        }
    }

}

#region Extensions

namespace AtCoderBeginnerContest150.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion