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 (GCC 5.4.1) (judge verdict: Accepted)


#include <stdio.h>

int gcd(int a, int b);

int main(){
    long long int a, b, c, d;
    long int i = 0;
    long long int cnt, cnt1;

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

    cnt = b;

    cnt -= b / c;
    cnt -= b / d;

    cnt += b / ((c * d) / gcd(c, d));


    cnt1 = a - 1;

    cnt1 -= (a - 1) / c;
    cnt1 -= (a - 1) / d;

    cnt1 += (a - 1) / ((c * d) / gcd(c, d));

    cnt -= cnt1;

    printf("%lld\n", cnt);

    return 0;

}

int gcd(int a, int b){
    int temp;

    if(a<b){
        temp = a;
        a = b;
        b = temp;    
    }

    int r = a % b;
    while(r!=0){
        a = b;
        b = r;
        r = a % b;
    }

    return b;
}