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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.ABC_150
{
    class D
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int[] nm = ReadInts();
            int n = nm[0];
            int m = nm[1];
            long[] array = ReadLongs();
            var vals = new HashSet<long>();
            for (int i = 0; i < n; i++) vals.Add(array[i]);
            var list = new List<long>();
            foreach(long val in vals) list.Add(val);
            long gcd = list[0];
            n = list.Count;
            for (int i = 1; i <n ; i++) gcd = GCD(gcd, array[i]);
            long lcm = gcd;
            for (int i = 0; i < n; i++)
            {
                lcm *= array[i] / gcd;
                if (lcm / 2 > m)
                {
                    WriteLine(0);
                    return;
                }
            }
            if (lcm % 2 == 1)
            {
                WriteLine(0);
                return;
            }
            for (int i = 0; i < n; i++)
            {
                long div = lcm / array[i];
                if (div % 2 == 0)
                {
                    WriteLine(0);
                    return;
                }
            }
            WriteLine((m - lcm / 2) / lcm + 1);
        }

        static long GCD(long a, long b)
        {
            if (b > a)
            {
                long temp = b;
                b = a;
                a = temp;
            }
            long c = b;
            do
            {
                c = a % b;
                a = b;
                b = c;
            } while (c > 0);
            return a;
        }

        static long LCM(long a, long b)
        {
            long c = GCD(a, b);
            return a * b / c;
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}