You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Constraints

* 1\leq A\leq B\leq 10^{18}
* 1\leq C,D\leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


A B C D


Output

Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Examples

Input

4 9 2 3


Output

2


Input

10 40 6 8


Output

23


Input

314159265358979323 846264338327950288 419716939 937510582


Output

532105071133627368
import java.util.Scanner;

public class Main{
  public static void main(String[] args){
    // 入力値の読み込み
    Scanner sc = new Scanner(System.in);
    long A = sc.nextLong()-1;
    long B = sc.nextLong();
    long C = sc.nextLong();
    long D = sc.nextLong();
    
    long A_C = A / C; // Cの個数
    long A_D = A / D; // Dの個数
    long A_CD = A / lcm(C, D); //最小公倍数
    long cntA = A_C + A_D - A_CD;
    
    long B_C = B / C; // Cの個数
    long B_D = B / D; // Dの個数
    long B_CD = B / lcm(C, D); //最小公倍数
    long cntB = B_C + B_D - B_CD;
    System.out.println(B - A - (cntB - cntA));
  }
  
  private static long lcm(long m, long n) {
    return m * n / gcd(m, n);
  }
  private static long gcd(long m, long n) {
    if(m < n) return gcd(n, m);
    if(n == 0) return m;
    return gcd(n, m % n);
  }
  
}