Contest Duration: - (local time) (100 minutes) Back to Home
C - Anti-Division /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 制約

• 1\leq A\leq B\leq 10^{18}
• 1\leq C,D\leq 10^9
• 入力はすべて整数である

### 入力

A B C D


### 出力

A 以上 B 以下の整数のうち、C でも D でも割り切れないものの個数を出力せよ。

### 入力例 1

4 9 2 3


### 出力例 1

2


5,7 が条件を満たします。

### 入力例 2

10 40 6 8


### 出力例 2

23


### 入力例 3

314159265358979323 846264338327950288 419716939 937510582


### 出力例 3

532105071133627368


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