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 System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

class Program
{
    static void Main(string[] args)
    {
        var wrong_answer = new wrong_answer();
        wrong_answer.Solve();
    }
}

public class wrong_answer
{
    const int INF = 1 << 30;
    const long INFL = 1L << 60;
    const int MOD = 1000000007;
    const int MOD2 = 998244353;

    myinout IO = new myinout();
    Math2 mmath = new Math2();

    //functions




    public void Solve()
    {
        //ここから
        var o = IO.longm;
        int n = (int)o[0];
        long m = o[1];
        var a = IO.longm;
        var lcm = a[0];
        var divideby2 = 0;
        for (int i = 0; i < n; ++i)
        {
            lcm = mmath.lcm(lcm, a[i]);
        }
        lcm /= 2;
        for (int i = 0; i < n; ++i)
        {
            var res = 0;
            while (a[i] % 2 == 0)
            {
                a[i] /= 2;
                res++;
            }
            if (i != 0)
            {
                if (res != divideby2||res==0)
                {
                    IO.wri(0);
                    return;
                }
            }
            else divideby2 = res;
        }

        var ans = m / lcm / 2;
        if (m / lcm % 2 == 1)
            IO.wri(ans+1);
        else IO.wri(ans);



    }

    public static bool NextPermutation<T>(ref T[] array, int start, int length)
       where T : IComparable
    {
        int end = start + length - 1;

        // 範囲が狭すぎる
        if (end <= start) return false;

        int last = end;
        while (true)
        {
            int pos = last--;

            if (array[last].CompareTo(array[pos]) < 0)
            {
                int i;
                for (i = end + 1; array[last].CompareTo(array[--i]) >= 0;) { }
                T tmp = array[last]; array[last] = array[i]; array[i] = tmp;
                Array.Reverse(array, pos, end - pos + 1);
                return true;
            }
            if (last == start)  // 最後の順列
            {
                Array.Reverse(array, start, end - start);
                return false;
            }
        }

        // ここに来ることはない
        throw new Exception("NextPermutation: Fatal error");
    }


}



//b-aで降順

public class Math2
{
    public long[] fact;
    public long[] invfact;
    public void factoricalmodset(long N, long MOD = 1000000007)
    {
        fact = new long[N + 1];
        invfact = new long[N + 1];
        fact[0] = 1;

        for (long i = 1; i <= N; ++i)
        {
            fact[i] = fact[i - 1] * i % MOD;
        }
        invfact[N] = pow(fact[N], MOD - 2);

        for (long i = N; i > 0; --i)
        {
            invfact[i - 1] = invfact[i] * i % MOD;
        }

    }

    public long nCr(long n, long r, long MOD = 1000000007)
    {
        return (fact[n] * invfact[r] % MOD * invfact[n - r] % MOD);
    }

    public long pow(long i, long n, long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }

    public long gcd(long i, long y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public long lcm(long i, long y)
    {
        return i * y / gcd(i, y);
    }

    public Dictionary<long, int> primefactorization(long N)
    {
        var ret = new Dictionary<long, int>();

        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2) ret[N] = 1;

        return ret;

    }

    public List<long> divisorenumrate(long N)
    {
        var ret = new List<long>();

        for (long i = 1; i * i <= N; ++i)
        {

            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }

        }

        return ret;

    }

    public void swap<T>(ref T a, ref T b)
    {
        var i = a;
        a = b;
        b = i;
    }

}

class myinout
{
    //in
    public string str => Console.ReadLine();

    public string[] strm => str.Split(' ');

    public long[] longm => strm.Select(long.Parse).ToArray();
    public int[] intm => strm.Select(int.Parse).ToArray();
    public char[] charm => str.ToArray();
    public double[] doublem => strm.Select(double.Parse).ToArray();
    public long long1 => longm[0];
    public int int1 => intm[0];
    public char char1 => charm[0];
    public double double1 => doublem[0];



    //out
    public void wri<T>(T i)
    {
        Console.WriteLine(i);
    }
    public void wri<T>(T[] i)
    {
        Console.WriteLine(string.Join(" ", i));
    }

    public void yn(bool i)
    {
        if (i) wri("Yes");
        else wri("No");
    }

}