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 Ruby (2.3.3) (judge verdict: Accepted)

A, B, C, D = gets.chomp.split.map(&:to_i)

# we calculate the numbers which can dividable by C, D, C*D

# (0, 3) -> 0
# (2, 3) -> 0
# (3, 3) -> 1
# (5, 3) -> 1
# (6, 3) -> 2
# numbers dividable by c under a.
# number of (i) .. i: 0 - a, i % c == 0
def nums(a, c)
  a / c
end

def gcd(a, b) 
  if (a < b) 
    # swap(a, b)
    tmp = a
    a = b
    b = tmp
  end

  if (b == 0) 
    return a
  end
  
  gcd(b, a % b)
end

cd = C * D / gcd(C, D) # lcm(C, D)

# 0..B
b = B - nums(B, C) - nums(B, D) + nums(B, cd)
# 0..A-1
a = (A-1) - nums(A-1, C) - nums(A-1, D) + nums(A-1, cd)

p b - a