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 Lua (5.3.2) (judge verdict: Accepted)

local function gcd(a,b)
    if b == 0 then
        return a
    else
        return gcd(b, a % b)
    end
end

local function gcdmany(tbl)
    local ans = tbl[1]
    for i=2,#tbl do
        ans = gcd(ans, tbl[i])
    end
    return ans
end

local function lcm(a, b)
    return a // gcd(a, b) * b
end

local function lcmmany(tbl)
    local ans = tbl[1]
    for i=2, #tbl do
        ans = lcm(ans, tbl[i])
    end
    return ans
end

---
local A, B, C, D = io.read("n", "n", "n", "n")
local function candiv(x)
    return (B // x) - ((A-1) // x)
end
local total = B - A + 1
local c_div = candiv(C)
local d_div = candiv(D)
local cd_lcm = lcm(C, D)
local cd_div = candiv(cd_lcm)
local ans = total - c_div - d_div + cd_div
print(ans)