Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

4 9 2 3

Sample Output 1

2

5 and 7 satisfy the condition.

Sample Input 2

10 40 6 8

Sample Output 2

23

Sample Input 3

314159265358979323 846264338327950288 419716939 937510582

Sample Output 3

532105071133627368

Solution in Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var a, b, c, d int
	fmt.Scan(&a, &b, &c, &d)
	cla := b / c
	csm := a / c
	csum := cla - csm
	if a%c == 0 {
		csum++
	}
	dla := b / d
	dsm := a / d
	dsum := dla - dsm
	if a%d == 0 {
		dsum++
	}
	lc := lcm(c, d)
	ela := b / lc
	esm := a / lc
	esum := ela - esm
	if a%d == 0 {
		esum++
	}
	fmt.Println(b - a + 1 - csum - dsum + esum)
}

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}

func lcm(a, b int) int {
	return a * b / gcd(a, b)
}