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>
#define max(X, Y) ((X) > (Y) ? (X) : (Y))
#define min(X, Y) ((X) < (Y) ? (X) : (Y))
#define swap(Type, X, Y) {Type _tmp = (X); (X) = (Y); (Y) = _tmp;}
typedef long long ll;

ll gcd(ll x, ll y);
ll lcm(ll x, ll y);

int main()
{
    ll a, b, c, d;
    ll l;

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

    l = lcm(c, d);

    printf("%lld\n", (b - a + 1) -
           ((b / c) + (b / d) - (b / lcm(c, d))) +
           (((a - 1) / c) + ((a - 1) / d) - ((a - 1) / lcm(c, d))));

    return 0;
}

ll gcd(ll x, ll y)
{
    if (x < y) {
        swap(ll, x, y);
    }

    ll r;

    while (y) {
        r = x % y;
        x = y;
        y = r;
    }

    return x;
}

ll lcm(ll x, ll y)
{
    return x / gcd(x, y) * y;
}