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.Text;
using System.Collections.Generic;
using static System.Math;
using System.Linq;
using static System.Array;
using System.Runtime.Serialization.Formatters.Binary;
using System.IO;

namespace AtcoderExpress
{


    class Program2
    {
        static long[] A;
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var N = NM[0];
            var M = NM[1];
            var flg = true;

            A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var a    = A[0];
            var resa = A[0] / 2;
            for (int i = 1; i < N; i++)
            {
                var b    = A[i];
                var resb = b / 2;
                if(resa > resb)
                {
                    var tmp  = a;
                    var tmpr = resa;
                    a    = b;
                    resa = resb;
                    b    = tmp;
                    resb = tmpr;
                }
                var K = resb - resa;
                //Console.WriteLine(a+" "+b+" "+K);
                //aX-bY = Kの解を一つ求める

                //解があることの確認
                var GCD = gcd(a, b);
                if (!(GCD == K || K == 0))
                {
                    flg = false;
                    break;
                }

                //拡張ユーグリッドでX,Yに解を入れる
                long X = 0;
                long Y = 0;
                if (K != 0)
                {
                    extgcd(b, a, ref Y, ref X);
                }

                var LCM = a * b / GCD;
                var rest = a * X+resa;
                resa = (rest + LCM * a)% LCM;
                a = LCM;
                
            }


            if (flg && M-resa >= 0)
            {
                Console.WriteLine((M-resa)/a+1);
            }
            else
            {
                Console.WriteLine(0);
            }
        }

        
        static long extgcd(long a, long b, ref long x,ref long y)
        {

            if (a < b) return extgcd(b, a, ref y, ref x);
            // xとyを入れ替え忘れないように注意

            if (b > 0)
            {
                long g = extgcd(b, a % b, ref y, ref x);
                y -= (a / b) * x;
                return g;
            }
            else
            {
                x = 1;
                y = 0;
                return a;
            }
        }

        static long gcd(long a, long b)
        {
            if (a < b) return gcd(b, a);
            if( b > 0)
            {
                return gcd(b, a%b);
            }
            else
            {
                return a;
            }
        }
    }
}