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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func init() {
	const maxWord = (1 << 30)
	buf := []byte{}
	sc.Buffer(buf, maxWord)
	sc.Split(bufio.ScanWords)
}

func input() string {
	sc.Scan()
	return sc.Text()
}

func gcd(x, y int) int {
	if x < y {
		x, y = y, x
	}
	for y > 0 {
		r := x % y
		x = y
		y = r
	}
	return x
}

func lcm(x, y int) int {
	return x * y / gcd(x, y)
}

func countNotMod(a, x, y int) int {
	c1 := a / x
	c2 := a / y
	c3 := a / lcm(x, y)
	return a - (c1 + c2 - c3)
}

func main() {
	a, _ := strconv.Atoi(input())
	b, _ := strconv.Atoi(input())
	c, _ := strconv.Atoi(input())
	d, _ := strconv.Atoi(input())

	ans := countNotMod(b, c, d) - countNotMod(a-1, c, d)
	fmt.Println(ans)
}