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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;

public class Main {

    static void solve() {
        int n = nextInt();
        int m = nextInt();
        List<Integer> aOrg = nextIntList(n);

        List<Integer> aHalf = aOrg.stream().map(e -> e / 2).collect(Collectors.toList());

        long lcm = aHalf.get(0);
        for (int i = 1; i < n; i++) {
            lcm = calLcm(lcm, aHalf.get(i));
        }
        // System.out.println("lcm=" + lcm);

        long ans = 0;
        for (long i = lcm; i <= m; i += 2 * lcm) {
            ans++;
        }

        // すべてのakで約数に含まれる2の数が同数で必要がある
        boolean ok = true;
        int numDouble = 0;
        for (int i = aHalf.get(0); i % 2 == 0; i /= 2) {
            numDouble++;
        }
        for (int i = 1; i < n; i++) {
            int num = 0;
            for (int j = aHalf.get(i); j % 2 == 0; j /= 2) {
                num++;
            }
            if (num != numDouble) {
                ok = false;
                break;
            }
        }

        if (ok) {
            out.println(ans);
        } else {
            out.println(0);
        }
    }

    static long calLcm(long a, long b) {
        if (a > b)
            return (a / gcd(a, b)) * b;
        else
            return (b / gcd(a, b)) * a;
    }

    static PrintWriter out;
    static Scanner sc;

    static int[][] newIntArray(int h, int w, int value) {
        int[][] ret = new int[h][w];
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                ret[i][j] = value;
            }
        }
        return ret;
    }

    static int nextInt() {
        return Integer.parseInt(sc.next());
    }

    static long nextLong() {
        return Long.parseLong(sc.next());
    }

    static String nextString() {
        return sc.next();
    }

    static int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    static List<Integer> nextIntList(int n) {
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(nextInt());
        }
        return list;
    }

    static List<Double> nextDoubleList(int n) {
        List<Double> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add((double) nextInt());
        }
        return list;
    }

    static List<Long> nextLongList(int n) {
        List<Long> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(nextLong());
        }
        return list;
    }

    static char[][] nextCharArray(int h, int w) {
        char[][] c = new char[h][w];
        for (int i = 0; i < h; i++) {
            String str = nextString();
            for (int j = 0; j < w; j++) {
                c[i][j] = str.charAt(j);
            }
        }
        return c;
    }

    static <T extends Comparable<? super T>> void sort(List<T> list) {
        Collections.sort(list);
    }

    // greatest common divisor
    static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    // baseのn乗を計算を返す
    static int pow(int base, int n) {
        int ret = 1;
        for (int i = 0; i < n; i++) {
            ret *= base;
        }
        return ret;
    }

    // return n^k mod m
    static long powMod(long n, long k, long m) {
        if (k == 0) {
            return 1;
        } else if (k % 2 == 1) {
            return powMod(n, k - 1, m) * n % m;
        } else {
            long tmp = powMod(n, k / 2, m);
            return tmp * tmp % m;
        }
    }

    // intをlength桁のbit文字列に変換
    static String toBinaryString(int input, int length) {
        return toBinaryString(input).substring(29 - length);
    }

    // intを29桁のbit文字列に変換
    static String toBinaryString(int input) {
        String ret = "";
        int max = 0x10000000;
        for (int i = 0; i < 29; i++) {
            int tmp = input / max;
            ret += tmp;
            input %= max;
            max /= 2;
        }
        return ret;
    }

    public static void main(String[] args) {
        out = new PrintWriter(System.out);
        sc = new Scanner(System.in);

        solve();

        out.flush();
        sc.close();
    }

}