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 C (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>

long long gcd(long long n, long long m);

int main()
{
    long long a, b, c, d;
    long long lc;

    scanf("%lld %lld", &a, &b);
    scanf("%lld %lld", &c, &d);

    lc = c * d / gcd(c, d);

    printf("%lld\n",
           (b - a + 1)
           - (b / c - (a - 1) / c)//cで割り切れる
           - (b / d - (a - 1) / d)//dで割り切れる
           + (b / lc - (a - 1) / lc));

    return 0;
}

long long gcd(long long n, long long m)
{
    if (m < n) {
        long long tmp = n;
        n = m;
        m = tmp;
    }

    while (n) {
        long long r = m % n;
        
        m = n;
        n = r;
    }

    return m;
}