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)

	// 全体の数
	totalNum := b - a + 1

	// 最小公倍数
	lcm := c * d / gcd(c, d)

	var cNum, dNum, eNum int
	if a%c == 0 {
		cNum = a/c - 1
	} else {
		cNum = a / c
	}
	if a%d == 0 {
		dNum = a/d - 1
	} else {
		dNum = a / d
	}
	if a%lcm == 0 {
		eNum = a/lcm - 1
	} else {
		eNum = a / lcm
	}

	// Cの倍数の数
	C := (b/c - cNum)
	// Dの倍数の数
	D := (b/d - dNum)
	// C,Dの公倍数の数
	CD := (b/lcm - eNum)

	ans := totalNum - (C + D - CD)
	fmt.Println(ans)
}

func gcd(x, y int) int {
	tmp := x % y
	if tmp > 0 {
		return gcd(y, tmp)
	} else {
		return y
	}
}